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Clairambault, Jean (INRIA)  Lecture Room 11  Fri, 1. Jul 16, 9:50 
"Heterogeneity and drug resistance in cancer cell populations: an evolutionary point of view with possible therapeutic consequences"  
I will present an evolutionary viewpoint on cancer, seen as the 2 time scales of (largetime) evolution in the genomes and of (shorttime) evolution in the epigenetic landscape of a constituted genome. These views, based on pioneering works by Lineweaver, Davies and Vincent (cancer as anatomically localised backward evolution in multicellular organisms, aka atavistic theory of cancer) and by Sui Huang and collaborators (revisited Waddington epigenetic landscape), respectively, may serve as guidelines to propose a global conception of cancer as a disease that impinges on all multicellular organisms, and they may lead to innovating therapeutic strategies. Druginduced drug resistance, the medical question we are tackling from a theoretical point of view, may be due to biological mechanisms of different natures, mere local regulation, epigenetic modifications (reversible, nevertheless heritable) or genetic mutations (irreversible), according to the extent to which the genome of the cells in the population is affected. In this respect, the modelling framework of adaptive dynamics presented here is more likely to correspond biologically to epigenetic modifications than to mutations, although eventual induction of emergent resistant cell clones due to mutations under drug pressure is not to be completely excluded. From the biologist's point of view, we study phenotypically heterogeneous, but genetically homogeneous, cancer cell populations under stress by drugs. The builtin targets for theoretical therapeutic control present in the phenotypestructured PDE models we advocate are not supposed to represent welldefined molecular effects of the drugs in use, but rather functional effects, i.e., related to cell death (cytotoxic drugs), or to proliferation in the sense of slowing down the cell division cycle without killing cells (cytostatic drugs). We propose that cell lifethreatening drugs (cytotoxics) induce by far more resistance in the highly plastic cancer cell populations than drugs that only limit their growth (cytostatics), and that a rational combination of the two classes of drugs may be optimised to propose innovating therapeutic control strategies to avoid the emergence of drug resistance in tumours.  

Obenauf, Anna (U. Wien)  Lecture Room 11  Fri, 1. Jul 16, 10:50 
"Unintended consequences of targeted cancer therapy: Therapy induced tumor secretomes fuel drug resistance and tumor Progression"  
The identification of molecular drivers in cancer has paved the way for targeted therapy. However, incomplete responses and relapse on therapy remain the biggest problem for improving patient survival. Evidence suggests that a tumor consists of a majority of cells that are sensitive to targeted therapy while few cells that are intrinsically resistant or poised to quickly adapt to drug treatment already preexist within this heterogeneous tumor population. Although a multitude of resistance mechanisms have been described, it was largely unknown how resistant cells behave in a heterogeneous tumor during treatment and whether a regressing tumor microenvironment could influence disease relapse. We found that targeted therapy with BRAF, ALK, or EGFR kinase inhibitors induces a complex network of secreted signals in drugstressed melanoma and lung adenocarcinoma cells. This therapyinduced secretome (TIS) stimulates the outgrowth, dissemination, and metastasis of drugresistant cancer cell clones in the heterogenous tumors and supports the survival of drugsensitive cancer cells, contributing to incomplete tumour regression. The vemurafenib reactive secretome in melanoma is driven by downregulation of the transcription factor FRA1. In situ transcriptome analysis of drugresistant melanoma cells responding to the regressing tumour microenvironment revealed hyperactivation of multiple signalling pathways, most prominently the AKT pathway. Dual inhibition of RAF and PI3K/AKT/mTOR pathways blunted the outgrowth of the drugresistant cell population in BRAF mutant melanoma tumours, suggesting this combination therapy as a strategy against tumour relapse. Thus, therapeutic inhibition of oncogenic drivers induces vast secretome changes in drugsensitive cancer cells, paradoxically establishing a tumour microenvironment that supports the expansion of drugresistant clones, but is susceptible to combination therapy.  

Ciccolini, Joseph (U. Aix Marseille)  Lecture Room 11  Fri, 1. Jul 16, 11:30 
"Not enough money on this earth: will pharmacometrics save oncology ?"  
Oncology has benefited from major groundbreaking innovations over the last 15years. Beyond standard chemotherapy, targeted therapies, antioangiogenics and now immune checkpoint inhibitors have all fueled high expectancies in terms of increased response rate and extended survival in patients. Of note, despite huge resources engaged now to better understand tumor biology and to identify relevant genetic and/or molecular biomarkers for choosing the best drugs, increase in survival has been mostly achieved in an incremental fashion so far, with the notable exception of CML and more recently of melanoma. The everincreasing number of druggable targets, along with the rise of new concepts such as cancer immunology, has contributed to a considerable complexification of the decisionmaking at bedside. Indeed, it is widely acknowledged now that combination therapy is the future of cancer treatment. As such, defining the optimal association between cytotoxics, radiotherapy, antiangiogenic drugs, targeted therapies and now immunotherapy is a major issue that remains to be addressed. Optimal solution will not be reached anymore by standard trialanderror empirical practice, owing to the nearinfinite number of possible combinations to be tested now that would require unsustainable efforts in terms of clinical development by pharmaceutical companies. In this respect, pharmacometrics (i.e., mathematical PK/PD models) could help to identify, using in silico simulations, a reduced number of working hypothesis to be tested in priority as part of clinical trials. Reviewing recent literature in the field and giving some examples in experimental and clinical oncology with chemotherapy, antiangiogenics and immunotherapy, we will discuss how pharmacometrics could indeed help to optimize anticancer treatments. The paradigm shift from empirical to more rationale practice is probably the next challenge in oncology.  

Vallette, Francois (U. Nantes)  Lecture Room 11  Fri, 1. Jul 16, 13:45 
"Biological analysis of the drug resistance acquisition in a glioma cell line"  
TBA  

Pouchol, Camille (INRIA)  Lecture Room 11  Fri, 1. Jul 16, 14:25 
"Optimal control of combined chemotherapies in phenotypestructured cancer cell populations evolving towards drug resistance"  
We investigate optimal therapeutical strategies combining cytotoxic and cytostatic drugs for the treatment of a solid tumour. The difficulty comes from the usual pitfalls of such treatments: emergence of drugresistance and toxicity to healthy cells. We consider an integrodifferential model for which the structuring variable is a continuous phenotype. Such models come from theoretical ecology and have been developed to understand how selection occurs in a given population of individuals. Two populations of healthy and cancer cells, both structured by a phenotype representing resistance to the drugs, are thus considered. The optimal control problem consists of minimising the number of cancer cells after some fixed time T. We first analyse the effect of constant doses on the longtime asymptotics through a Lyapunov functional. The optimal control problem is solved numerically, and for large T, we also theoretically determine the optimal strategy in a restricted class of controls.  

Berger, Walter (MedUni Wien) & Mohr, Thomas (MedUni Wien)  Lecture Room 11  Fri, 1. Jul 16, 15:20 
"Modeling factors contributing to glioblastoma aggressiveness"  
Glioblastoma represents the most frequent and aggressive primary brain tumor. Despite intense research and availability of extended in silico data, the mean patient survival after diagnosis is only around 15 months. Classical alkylating chemotherapy with concomitant radiation is still the standard therapeutic approach. This demonstrates that the revolution of modern precision medicine based on “big data” strategies has not resulted in approved therapeutic options and patient prognosis in this deadly disease so far. This implies that simple big data collection with bioinformatic evaluation might not be sufficient to translate into clinical benefit and close cooperations between systems biology and whet lab research is essential. Accordingly, we focus in our research cooperation on a multistrategy approach focusing on a tight integration of 1) largescale biobanking of viable malignant cells and cancer stem cells, 2) wetlab cell and molecular biology and xenograft experiments; 3) extended omics analysis and 4) advanced computational biology methods. Regarding molecular factor driving tumor aggressiveness, data on a recently discovered noncoding mutation in the promoter of the telomerase reverse transcriptase (TERT) gene in human glioblastoma will be elucidated. Additionally, using publicly available gene expression profiles of glioblastoma patients we tried to bridge the existing gap of understanding the association of individual genes/mutations to complex physiological processes by the systematic investigation of the observed relationship between gene products and clinical traits. A weighted gene coexpression network approach (WGCNA) has been proposed to reconstruct gene coexpression networks in terms of largescale gene expression profiles and as well as for the distinction genes potentially driving key cellular signaling pathways based on the centrality – lethality theorem. The WGCNA approach provides a functional interpretation in Systems Biology and leads to new insights into cancer pathophysiology. Here, we applied a systematic framework for constructing gene coexpression networks (modules) and pinpointing key genes that may drive tumorigenesis and progression in different subclasses of GBM. Microarray data were downloaded from The Cancer Genome Atlas, corrected for batch effects using ComBat and normalized using rma and quantil normalization. Outliers were excluded using coexpression network parameters and coexpression network similarity. The resulting dataset was stratified according to the classification of Verhaak et al. and subjected to comparative Weighted Gene Coexpression analysis. The resulting modules were tested for module preservation across GBM subtypes using the connectivity and density measures. Modules of interest (both preserved and differentially interconnected) were analyzed for biological function using Term Enrichment Analysis methods and correlated to clinical traits (e.g. survival) to identify potential key driving coexpression networks. The lead modules will be then subject to cell biological and in vivo evaluation in glioblastoma models. In summary this multidisciplinary approach offers novel insights into glioblastoma aggressiveness and might uncover novel therapeutic targets.  

Lorenzi, Tommaso (U. St. Andrews)  Lecture Room 11  Fri, 1. Jul 16, 16:00 
" Observing the dynamics of cancer cell populations through the mathematical lens of structured equations "  
A growing body of evidence supports the idea that solid tumours are complex ecosystems populated by heterogeneous cells, whose dynamics can be described in terms of evolutionary and ecological principles. In this light, it has become increasingly recognised that models that are akin to those arising from mathematical ecology can complement experimental cancer research by capturing the crucial assumptions that underlie given hypotheses, and by offering an alternative means of understanding experimental results that are currently available. This talk deals with partial differential equations modelling the dynamics of structured cancer cell populations. Analyses and numerical simulations of these equations help to uncover fresh insights into the critical mechanisms underpinning tumour progression and the emergence of resistance to anticancer therapies.  

Xu, Zhou (U. UPMC Paris VI)  Lecture Room 11  Sat, 2. Jul 16, 9:30 
"Telomere length dynamics and senescence heterogeneity: when size matters"  
Failure to maintain telomeres leads to their progressive erosion at each cell division. This process is heterogeneous but eventually triggers replicative senescence, a pathway shown to protect from unlimited cell proliferation, characteristic of cancer cells. However, the mechanisms underlying its variability and its dynamics are not characterized. Here, we used a microfluidicsbased livecell imaging assay to investigate replicative senescence in individual Saccharomyces cerevisiae cell lineages. We show that most lineages experience an abrupt and irreversible transition from a replicative to an arrested state, contrasting with the common idea of a progressive transition. Interestingly, senescent lineages displayed an important heterogeneity in their timing to enter senescence despite starting from the same initial telomeres. To understand this, we built several mathematical models, successively adding layers of molecular details. We find that, in a stochastic model where the first telomere reaching a critical short length triggers senescence, the variance of the initial telomere distribution mostly accounts for senescence heterogeneity. Unexpectedly, the residual heterogeneity is structurally built in the asymmetrical telomere replication mechanism. We then theoretically studied different senescence regimes, depending on the initial telomere variance, and provided analytical solutions to derive senescence onset from telomere length. Furthermore, the microfluidics approach also revealed another class of lineages that undergo frequent reversible cellcycle arrests. Cells with this phenotype persist only at low frequency in bulk cultures but could initiate both genomic instability and postsenescence survival through adaptation mechanisms. These data suggest that another source of heterogeneity of senescence onset consists of stochastic telomere damages that may be the basis of cancer emergence.  

Almeida, Luis (U. UPMC Paris)  Lecture Room 11  Sat, 2. Jul 16, 10:30 
"Mathematical models for epithelial tissue integrity restoration"  
We will present work on the mechanisms used for establishing or restoring epithelial integrity which are motivated by experimental work on development and wound healing in Zebrafish and drosophila and on gap closure in monolayers of MDCK cells or keratinocytes. These works concern mathematical modeling of the dynamics of epithelial tissues pulled by lamellipodal crawling or the contraction of actomyosin cables at the gap boundary. We are particularly interested in the influence of the wound/gap geometry and of the adhesion to the substrate on the closure mechanism.  

Stiehl, Thomas (U. Heidelberg)  Lecture Room 11  Sat, 2. Jul 16, 11:10 
"Heterogeneity in acute leukemias and its clinical relevance – Insights from mathematical modeling"  
Acute leukemias are cancerous diseases of the blood forming (hematopoietic) system. A hallmark of acute leukemias is heterogeneity of their clinical course. Similar as the hematopoietic system, leukemias originate from a small population of leukemic stem cells that resist treatment and trigger relapse. Recent gene sequencing studies demonstrate that the leukemic cell mass is composed of multiple clones the contribution of which changes over time. We propose compartmental models of hierarchical cell populations to study interaction of leukemic and healthy cells. The models are given as nonlinear ordinary differential equations. They include different feedback mechanisms that mediate competition and selection of the leukemic clones and the decline of healthy cells. Examples for considered mechanism are hormonal (cytokine) feedback loops, competition within the stem cell niche and overcrowding of the bone marrow space. A combination of computer simulations and patient data analysis is applied to provide insights in the following questions: (1) Which mechanisms allow leukemic cells to outcompete their benign counterparts? (2) How do properties of leukemic clones in terms of selfrenewal and proliferation change during the course of the disease? What is the impact of treatment on clonal properties? (3) How do leukemic stem cell parameters affect the clinical course and patient prognosis? (4) What is the impact of leukemic cell properties on the number of leukemic clones and their genetic interdependence? (5) How does responsiveness of leukemic cells to signals of healthy hematopoiesis influence treatment response? Do interindividual differences in signal sensitivity of leukemic cells matter? The talk is based on joint works with Anna MarciniakCzochra (Institute of Applied Mathematics, Heidelberg University), Anthony D. Ho, Natalia Baran and Christoph Lutz (Heidelberg University Hospital).  

Hanson, Shalla (U. Duke)  Lecture Room 11  Sat, 2. Jul 16, 13:30 
"Toxicity Management in CAR T cell therapy for BALL: Mathematical modelling as a new avenue for improvement"  
Advances in genetic engineering have made it possible to reprogram individual immune cells to express receptors that recognise markers on tumour cell surfaces. The process of reengineering T cell lymphocytes to express Chimeric Antigen Receptors(CARs), and then reinfusing the CARmodified T cells into patients to treat various cancers is referred to as CAR T cell therapy. This therapy is being explored in clinical trials  most prominently for B Cell Acute Lymphoblastic Leukaemia (BALL), a common B cell malignancy, for which CAR T cell therapy has led to remission in up to 90% of patients. Despite this extraordinary response rate, however, potentially fatal inflammatory side effects occur in up to 10% of patients who have positive responses. Further, approximately 50% of patients who initially respond to the therapy eventually relapse. Significant improvement is thus necessary before the therapy can be made widely available for use in the clinic. To inform future development, we develop a mathematical model to analyze the interaction dynamics between CAR T cells, inflammatory toxicity, and individual patients' tumour burdens in silico. This talk outlines an underlying system of coupled ordinary differential equations, designed based on wellknown immunological principles and widely accepted views on the mechanism of toxicity development in CAR T cell therapy for BALL, to form novel hypotheses on key factors in toxicity development, and reports in silico outcomes in relationship to standard and recently conjectured predictors of toxicity in a heterogeneous, randomly generated patient population. Our initial results and analyses are consistent with and connect immunological mechanisms to the clinically observed, counterintuitive hypothesis that initial tumour burden is a stronger predictor of toxicity than is the dose of CAR T cells administered to patients. We outline how the mechanism of action in CAR T cell therapy can give rise to such nonstandard trends in toxicity development, and demonstrate the utility of mathematical modelling in understanding the relationship between predictors of toxicity, mechanism of action, and patient outcomes.  

Eder, Thomas (Ludwig Boltzmann Institute)  Lecture Room 11  Sat, 2. Jul 16, 14:00 
"The Normalization Visualization Tool or how to choose an adequate normalization strategy for RNASeq experiments"  
Differential gene expression analysis between healthy and cancer samples is a common task. In order to identify differentially expressed genes, it is crucial to normalize the raw count data of RNASeq experiments. There are multiple normalization methods available but all of them are based on certain assumptions. These may or may not be suitable for the type of data they are applied on and especially if an experiment compares gene expression levels of healthy vs. rapidly growing tumor cells, the assumptions of nondifferentially expressed genes or equal amounts of mRNA might not apply. Researchers therefore need to select an adequate normalization strategy for each RNASeq experiment. This selection includes exploration of different normalization methods as well as their comparison. We developed the NVT package, which provides a fast and simple way to analyze and evaluate multiple normalization methods via visualization and representation of correlation values, based on a userdefined set of uniformly expressed genes.  

Botesteanu, DanaAdriana (U. Maryland)  Lecture Room 11  Sat, 2. Jul 16, 14:30 
"Modeling the Dynamics of Highgrade Serous Ovarian Cancer Progression for Transvaginal UltrasoundBased Screening and Early Detection"  
Highgrade serous ovarian cancer (HGSOC) represents the majority of ovarian cancers and disease recurrence is common, and leads to incurable disease. Emerging insights into disease progression suggest that timely detection of low volume HGSOC, not necessarily also early stage, should be the goal of any screening study. However, numerous transvaginal ultrasound (TVU) detectionbased studies aimed at detecting lowvolume ovarian cancer have not yielded reduced mortality rates and thus invalidate TVU as an effective HGSOC monitoring strategy in improving overall survival. Our mathematical modeling approach proposes a quantitative explanation behind the reported failure of TVU to improve HGSOC lowvolume detectability and overall survival rates. We develop a novel in silico mathematical assessment of the efficacy of a unimodal TVU monitoring regimen as a strategy aimed at detecting lowvolume HGSOC in cancerpositive cases, defined as cases for which the inception of the first malignant cell has already occurred. Focusing on a malignancy poorly studied in the mathematical oncology community, our model recapitulates the dynamic, temporal evolution of HGSOC progression, and is characterized by several infrequent, ratelimiting events. Our results suggest that multiple frequency TVU monitoring across various detection sensitivities does not significantly improve detection accuracy of HGSOC in an in silico cancerpositive population. This is a joint work with Doron Levy (University of Maryland, College Park) and JungMin Lee (Women’s Malignancies Branch, National Cancer Institute)  

Lorz, Alexander (U. Paris VI & KAUST)  Lecture Room 11  Sat, 2. Jul 16, 15:20 
"Population dynamics and therapeutic resistance: mathematical models"  
We are interested in the Darwinian evolution of a population structured by a phenotypic trait. In the model, the trait can change by mutations and individuals compete for a common resource e.g. food. Mathematically, this can be described by nonlocal LotkaVolterra equations. They have the property that solutions concentrate as Dirac masses in the limit of small diffusion. We review results on longterm behaviour and small mutation limits. A promising application of these models is that they can help to quantitatively understand how resistances against treatment develop. In this case, the population of cells is structured by how resistant they are to a therapy. We describe the model, give first results and discuss optimal control problems arising in this context.  

Gulisashvili, Archil (U. Ohio)  Lecture Room 13  Tue, 5. Jul 16, 9:00 
"Peter Laurence as friend and collaborator"  
My talk is dedicated to the memory of Peter Laurence, whose un timely death has left a void in many peoples hearts. Peter was a truly great mathematician and a wonderful person. In the rst part of the talk, Peter's scientic biography will be presented. I will also share personal recollections of my meetings with Peter facetoface and in the skype world. The second part of the talk will be more mathematical. I will speak about my joint work with Peter on Riemannian geometry of the Heston model, which is one of the classical stock price models with stochastic volatility. My collaboration with Peter resulted in the paper "The Heston Riemannian distance function", which was published in 2014 by "Journal de Mathematiques Pures et Appliquees". In the paper, we found two explicit formulas for the Riemannian Heston distance, using geometrical and analytical methods. Geometrical approach is based on the study of the Heston geodesics, while the analytical approach exploits the links between the Heston distance function and a similar distance function in the Grushin plane. We also proved a partial large deviation principle for the Heston and the Grushin models. After completing our work on the paper, we started discussing future projects, but fate interfered. I will finish the talk by briefly presenting my recent results on the distance to the line in the Heston plane, and how such results can be used in nancial mathematics. Peter's scientic in uence continues after his untimely departure from this world.  

Vargiolu, Tiziano (U. Padova)  Lecture Room 13  Tue, 5. Jul 16, 10:30 
"Additive Models for Forward Curves in Multicommodity Energy Markets"  
In contrast to geometric models, additive models in energy markets, in particular in markets where forward contracts are delivered during a period like electricity and natural gas, allows easily the computation of forward prices in closed form. Moreover they naturally allow the presence of negative prices, which start to appear more and more frequently in electric markets. In this paper we present an additive multicommodity model which allows for meanreverting dynamics consistent with noarbitrage, based on the observed prices of forward contracts based on the mean on a period, which are the most liquid instruments in natural gas and electricity markets. This allows to compute the price of more complex derivatives and of risk measures of portfolios in a way which is consistent with market data. Joint work with Luca Latini.  

Callegaro, Giorgia (U. Padova)  Lecture Room 13  Tue, 5. Jul 16, 11:00 
"Utility Indierence Pricing and Hedging for Structured Contracts in En ergy Markets"  
In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indierence pricing approach in a general incomplete multivariate market model driven by nitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyers utility indierence price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, we ob tain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided.  

Veraart, Almut (Imperial College)  Lecture Room 13  Tue, 5. Jul 16, 14:00 
"Ambit stochastics in Energy Markets"  
This talk gives an introduction to the area of ambit stochastics with a particular focus on applications in energy markets. In particular, we will describe models for energy spot and forward prices based on socalled ambit elds. These models are very exible and at the same time highly analytically tractable making them interesting from a mathematical perspective, but also very useful for applications.  

Ziel, Florian (EuropaUniversitat Viadrina)  Lecture Room 13  Tue, 5. Jul 16, 15:30 
"Electricity Price Forecasting using Sale and Purchase Curves: The X Model"  
Our paper aims to model and forecast the electricity price in a com pletely new and promising style. Instead of directly modeling the electricity price as it is usually done in time series or data mining approaches, we model and utilize its true source: the sale and purchase curves of the electricity ex change. We will refer to this new model as XModel, as almost every deregulated electricity price is simply the result of the intersection of the electricity supply and demand curve at a certain auction. Therefore we show an approach to deal with a tremendous amount of auction data, using a subtle data processing technique as well as dimension reduction and lasso based estimation methods. We incorporate not only several known features, such as seasonal behavior or the impact of other processes like renewable energy, but also completely new elaborated stylized facts of the bidding structure. Our model is able to cap ture the nonlinear behavior of the electricity price, which is especially useful for predicting huge price spikes. Using simulation methods we show how to 11 derive prediction intervals. We describe and show the proposed methods for the dayahead EPEX spot price of Germany and Austria. Joint work with Rick Steinert. 12  

Kostrzewski, Maciej (U. Krakau)  Lecture Room 13  Tue, 5. Jul 16, 16:00 
"Bayesian Analysis of Electricity Spot Price under SVLEJX Model"  
In the study, the Bayesian stochastic volatility model with normal errors, a leverage eect, a jump component and exogenous variables (SVLEJX) is proposed. This Bayesian framework, founded upon the idea of latent variables is computationally facilitated with Markov Chain Monte Carlo methods. In this paper, the Gibbs sampler is employed. The SVLEJX structure is applied to model electricity spot price. The results of Bayesian estimation, jump detection and forecasting are presented and discussed. The series of waiting times between two consecutive jumps is also of interest in the paper. Periods of no jumps alternating with the ones of frequent jumps could be indicative of existence of the jump clustering phenomenon. The impact of exogenous variables on electricity spot price dynamic is explored. Moreover, the leverage eect and the stochastic volatility clustering are tested.  

Gruet, Pierre (EDF)  Lecture Room 13  Tue, 5. Jul 16, 16:30 
"Ecient Estimation in a TwoFactor Model from Historical Data: Appli cation to Electricity Prices"  
We aim at modeling the prices of forward contracts on electricity, by adopting a stochastic model with two Brownian motions as stochastic factors to describe their evolution over time. In contrast to the model of (Kiesel et al., 2009), the diusion coecients are stochastic processes; the one of the rst factor is left totally unspecied, and the other one is the product of an unspecied process and of an exponential function of time to the maturity of the forward contract, which allows to account for some shortterm eect in the increase of volatility. We will consider that price processes following this model are observed simultaneously, at n observation times, over a given time interval [0; T]. The time step T=n between two observation times is small with respect to T, in the asymptotics n ! 1. We estimate some parameter of the exponential factor in volatility, with the usual rate, and we explain how it can be estimated eciently in the CramrRao sense. We are also able to estimate the trajectories of the two unspecied volatility processes, using nonparametric methods, with the standard rate of convergence. Numerical tests are performed on simulated data and on real prices data, so that we may see how appropriate our twofactor model is when applied to those data. Joint work with Olivier Feron (EDF, France) and Marc Homann (Universite ParisDauphine).  

Palczewski, Jan (U. Leeds)  Lecture Room 13  Tue, 5. Jul 16, 17:00 
"Energy Imbalance Market Call Options and the Valuation of Storage"  
In this paper we assess the real option value of operating reserve pro vided by an electricity storage unit. The contractual arrangement is a series of American call options in an energy imbalance market (EIM), physically covered and delivered by the store. The EIM price is a general regular onedimensional Diffusion. Necessary and sucient conditions are provided for a unique optimal strategy and value. We provide a straightforward procedure for numerical solution and several examples. Joint work with John Moriarty.  

Kholodnyi, Valerie (Verbund)  Lecture Room 13  Wed, 6. Jul 16, 9:00 
"Extracting ForwardLooking MarkedImplied RiskNeutral Probabilities for the Intraday Power Spots in the Unied Framework of the NonMarkovian Approach"  
Benets of a unied modeling framework The nonMarkovian approach as a unied framework for the consistent modeling of power spots, forwards and swaps Extracting forwardlooking marketimplied riskneutral probabilities for the intraday hourly and intrahourly power spots from a single or multiple market forward curves Taking into account: { daily, weekly, annual and metaannual cyclical patterns, { linear and nonlinear trends, { upwards and downwards spikes, { positive and negative prices Interpolating and extrapolating power market forward curves: { intrahourly, hourly, daily, weekly and monthly power forward curves, { extending power market forward curves beyond their liquidity hori zons Modeling the German Intraday Cap Week Futures as an hourly strip of Asian call options on forwards on the intraday hourly power spots  

Krühner, Paul (TU Wien)  Lecture Room 13  Wed, 6. Jul 16, 10:30 
"Representation of Innite Dimensional Forward Price Models in Com modity Markets"  
The Heath Jarrow Morton (HJM) approach treats the family of fu tures  written on a commodity as primary assets and models them directly. This approach has been used for the modelling of future prices in various markets by several authors and it has found its use by practitioners. We derive several representations of possible future dynamics and implications on futures and the spot from an innite dimensional point of view. To be more specically, let us de note the spot price by St and the future prices by ft(x) := E(St+xjFt); x; t 0. Due to the wellknown Heath Jarrow Morton Musiela drift condition the dy namics of ft cannot be specied arbitrarily under the pricing measure. We model it by dft = @xftdt + tdLt in a suitable function space where L is some Levy process. Then we derive a series representation for the futures in terms of the spot price process and OrnsteinUhlenbeck type processes, we represent the spot as a Levysemistationary process and nd formulae for the correlation between the spot and futures.  

Ronn, Ehud (U. Texas)  Lecture Room 13  Wed, 6. Jul 16, 11:00 
"Risk and Expected Return in the OilFutures Market"  
This paper considers two elements of the oilfutures markets: Ex pected return and risk. 3 With respect to expected return, the paper presents a parsimonious and theoreticallysound basis for extracting forwardlooking measures of equity and commodity betas, and the riskpremium on crudeoil futures contracts. Dening forwardlooking betas as perturbations of historical estimates, we use the mar ket prices of equity, index and commodity options under a singlefactor market model to estimate the appropriate forwardlooking perturbation to apply to the historical beta. This permits us to compute forwardlooking term structures of equity and commodity betas. In the commodity arena, we use both one and twofactor models to obtain estimates of a forwardlooking measure of the correlation between crudeoil and the S&P 500. Combining these with forward looking (i.e., implied) volatilities on commodities and stockmarket indices, we utilize these forwardlooking betas and correlations to provide an exante esti mate of the expected future crudeoil spot price through the use of an equity exante risk premium and the conditional CAPM. With respect to risk, we use the market prices for crudeoil futures options and the prices of their underlying futures contracts to calibrate the volatility skew using the Merton (1976) jumpdiusion optionpricing model. We demon strate the jumpdiusion parameters bear a close relationship to concurrent eco nomic, nancial and geopolitical events. This produces an informationallyrich structure covering the time period of the turbulent post2007 time period.  

Schmidt, Thorsten (U. Freiburg)  Lecture Room 13  Wed, 6. Jul 16, 14:00 
"Fundamentals of Energy Markets"  
We review current approaches of energy markets and start by studying absence of arbitrage in an innitedimensional setting. Once this is achieved we consider also structural frameworks for electricity forwards, taking into account relevant risk factors, like capacity and fuels prices. In a polynomial framework we obtain tractable pricing formulas. This is joint work with Christa Cuchiero and Julian Wergieluk  

Erwan, Pierre (EDF)  Lecture Room 13  Wed, 6. Jul 16, 15:30 
"Numerical Approximation of a CashConstrained Firm Value with In vestment Opportunities"  
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cashconstrained rms. The value function is proved to be the unique viscosity solution of the associated HamiltonJacobiBellman equa tion. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deter ministic approximation of the related HJB variational inequality is provided. We nally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies. Joint work with Stephane Villeneuve and Xavier Warin.  

Mora, Andres (U. de los Andes)  Lecture Room 13  Wed, 6. Jul 16, 16:30 
"Risk Quantication for Commodity ETFs: Backtesting ValueatRisk and Expected Shortfall"  
This paper studies the risk assessment of alternative methods for a wide variety of Commodity ETFs. We implement wellknown as well as and recently proposed backtesting techniques for both valueatrisk (VaR) and ex pected shortfall (ES) under extreme value theory (EVT), parametric, and semi nonparametric techniques. The application of the latter to ES was introduced in this paper and for this purpose we derive a straightforward closed form of ES. We show that, for the condence levels recommended by Basel Accords, EVT and GramCharlier expansions have the best coverage and skewedt and GramCharlier the best relative performance. Hence, we recommend the ap plication of the above mentioned distributions to mitigate regulation concerns about global nancial stability and commodities risk assessment. Joint work with Esther Del Brio and Javier Perote.  

Deschatre, Thomas (EDF)  Lecture Room 13  Wed, 6. Jul 16, 16:30 
"On the Control of the Dierence between two Brownian Motions: A Dynamic Copula Approach"  
We propose new copulae to model the dependence between two Brow nian motions and to control the distribution of their dierence. Our approach is based on the copula between the Brownian motion and its re ection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copu lae. These copulae allow for the survival function of the dierence between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. We derive two models based on the structure of the Re ection Brownian Copula which present two states of correlation ; one is directly based on the re ection of the Brownian motion and the other is a local correlation model. These models can be used for risk management and option pricing in commodity energy markets.  

Lässig, Yves (U. Freiburg)  Lecture Room 13  Wed, 6. Jul 16, 17:00 
"Control of an Energy Storage under Stochastic Consumption"  
We consider a typical optimal control problem from the viewpoint of an energy utility company. The company faces a varying energy demand of its associated consumers, modelled by a stochastic process. Demands can be satised by either buying energy at an exchange or the utilisation of an energy storage system. Furthermore the company is able to buy energy on a larger scale  than needed to satisfy demands  and enlarge the storage level or respectively sell energy from the storage directly to the market. In contrast to previous lit erature the storing facility therefore serves as a hedge against market price and demand volume risks and is not considered isolated from other market activities of the operator. Therefor the value function  which can be interpreted as a real option value of the storage  diers from classical optimal storage control prob lems and delivers a better quantication of the storage value for a specic user. We formulate a stochastic control problem including these features and pay par ticular attention to the operational constraints of the storage. Furthermore we will introduce methods to model the energy spot price and the consumption rate stochastically. Subsequently we will derive a candidate for the optimal policy, verify its optimality and solve the arising HamiltonJacobiBellman equation for the value function numerically using a novel nite elements discretization.  

Davison, Matt (U. Western Canada)  Lecture Room 13  Thu, 7. Jul 16, 9:00 
"A Real Options Analysis of the Relation between Ethanol Producers and Corn and Ethanol Markets"  
In recent years, for a variety of reasons, it has become popular in North American to produce Ethanol (for blending with gasoline) from Corn. The resulting industrial process can be modelled as an option on the "crush spread" between Ethanol and Corn. Under a price  taker assumption, real options models of ethanol production can be made incorporating random corn and ethanol prices. In the rst part of my talk I will report work done in my group, together with Natasha Burke and Christian Maxwell, on creating and solving real options models of the cornethanol industry. These models provide interesting insights about the relationship between corn prices, ethanol prices, and their correlation with valuations and operational decisions. Using a jump process, we are also able to incorporate the impact of random changes in government subsidies on the valuation and operation of ethanol facilities. However, while in the relatively fragmented US corn ethanol market it might be (just) reasonable to model any given ethanol producer as a price taker, all producers taken together do have market impact. In the second part of my talk I report work, joint with Nicolas Merener (Universidad Torcuata di Tella, Buenos Aires) on creating tractable models for this price impact. I will also sketch our progress toward solving the models and confronting them with data.  

Lange, Nina (U. Sussex)  Lecture Room 13  Thu, 7. Jul 16, 10:30 
"Presence of Joint Factors in Term Structure Modelling of Oil Prices and Exchange Rates"  
The paper studies the timevarying correlation between oil prices and exchange rates and their volatilities. Generally, when the value of the dollar weakens against other major currencies, the prices of commodities tend move higher. The signicance of this relationship has increased since 2000 with indica tions of structural breaks around the beginning of the socalled nancialization of commodity marketsregime and again around the beginning of the nancial crisis. Also the correlation between the volatility of oil prices and the volatil ity of exchange rates seems to experience the same behaviour as the returns correlation. This paper introduces and estimates a term structure model for futures contracts and option contracts on WTI crude oil and EURUSD. The model is tted a panel data of futures prices covering 20002013. The model allows for stochastic volatility and correlation and identies how the number of joint factors increases over time.  

Pflug, Georg (U. Wien)  Lecture Room 13  Thu, 7. Jul 16, 11:00 
"Pricing of Electricity Contracts"  
It is typical for electricity contracts, that the time of concluding the contract and the time of delivery are quite dierent. For this reason, these contracts are subject to risk and risk premia are and must be part of the pricing rules. In the rst part of the talk, we investigate electricity futures to nd out pricing rules, which the market is applying, such as the distortion priciple, the certainty equivalence priciple or the ambiguity priciple. We then investigate a noarbitrage principle in the presence of capacity contraints on production and storage. We review then the idea of acceptance pricing and indierence pricing using a concrete model. Finally we present a bilevel problem, where the pricing decision depends on the behavioral pattern of the counterparty. Some algorithmic aspects will be discussed as well. Joint work with Raimund Kovacevic  

Sgarra, Carlo (U. Politecnico di Milano)  Lecture Room 13  Thu, 7. Jul 16, 14:00 
"A Branching Process Approach to Power Markets"  
Energy markets, and in particular, electricity markets, exhibit very peculiar fea tures. The historical series of both futures and spot prices include seasonality, mean reversion, spikes and small uctuations. Very often a stochas tic volatility dynamics is postulated in order to explain their high degree of variability. Moreover, as it also appears in other kind of markets, they exhibit also the USV (Unspanned Stochastic Volatility) phaenomenon [7]. After the pioneering paper by Schwartz, where an OrnsteinUhlenbeck dy namics is assumed to describe the spot price behavior, several dierent ap proaches have been investigated in order to describe the price evolution. A comprehensive presentation of the literature until 2008 is oered in the book by F.E. Benth, J. SaltyteBenth and S. Koekebakker [4]. High frequency trading, on the other hand, introduced some new features in com modity prices dynamics: in the paper by V. Filimonov, D. Bicchetti, N. Maystre and D. Sornette [5] evidence is shown of endogeneity and structural regime shift, and in order to quantify this level the branching ratio is adopted as a measure of this endoge nous impact and a Hawkes processes dynamics is assumed as a reasonable modelling framework taking into account the self exciting properties [1]. The purpose of the present paper is to propose a new modeling framework including all the above mentioned features, still keeping a high level of tractabil ity. The model considered allows to obtain the most common derivatives prices in closed or semiclosed form. Here with semiclosed we mean that the Laplace transform of the derivative price admits an explicit expression. The models we are going to introduce can describe the prices dynamics in two dierent forms, that can be proved to be equivalent: the rst is a representation based on random elds, the second is based on Continuous Branching Processes with Immigration (CBI in the following). The idea of adopting a random elds framework for power prices description is not new: O.E. BarndorNielsen, F.E. Benth and A. Veraart introduced the Ambit Fields to this end, showing how this approach can provide a very exible and still tractable setting for derivatives pricing [2], [3]. A model based on CBI has been proposed recently by Y. Jiao, C. Ma and S. Scotti in view of short interest rate modelling, and in that paper it was shown that, with a suitable choice of the Levy process driving the CBI dynamics, the model can oer a signicant extension of the poular CIR model [6]. We shall propose two dierent types of dynamics for the prices evolution. The rst class will be named the Arithmetic models class, and the second will be named the Geometric model class; in adopting the present terminology we are following the classication proposed in [4]. We shall compare the advan tages and the limitations implied by each model class and we shall investigate the risk premium behavior for each of the classes considered. The paper will be organized as follows: in the rst Section we introduce the stochas tic processes we are going to consider, while in the second Section we discuss how these pro cesses can be successfully applied to power markets description. In the third Sec tion we derive some closed formulas for Futures and Option prices when the underlying dynamics is assumed to be given by the model introduced. In the fourth Section we shall investigate the risk premium term structure for the models under consideration. In the fth Section, we provide some suggestions about estimation and/or calibration methods for the same model. We complete our presentation with a statistical analysis on the two cases and some numer ical illustrations of the results obtained. In the nal section we provide some concluding remarks and discuss futures extensions of the present work. Joint work with Ying Jiao, Chunhua Ma and Simone Scotti. References: [1] Bacry, E., Mastromatteo, J., Muzy, J.F. Hawkes Processes in Finance, PREPRINT(2015). [2] BarndorNielsen, O.E., Benth, F.E., Veraart, A. Modelling energy spot prices by volatil ity modulated Levy driven Volterra processes, Bernoulli, 19, 803845 (2013). [3] BarndorNielsen, O.E., Benth, F.E., Veraart, A. Modelling Electricity Fu tures by Am bit Fields, Advances in Applied Probability, 46 (3), 719745 (2014). [4] Benth, F.E., SaltyteBenth J., Koekebakker S. Stochastic Modelling of Elec tricity and Related Markets , World Scientic, Singapore (2008). [5] Filimonov, V., Bicchetti, D., Maystre, N., Sornette, D. Quantication of the High Level of Endogeneity and Structural Regime Shifts in Commodity Markets, PREPRINT (2015). [6] Jiao, Y., Ma, C., Scotti, S. AlphaCIR Model with Branching Processes in Sovereign Interest Rate Modelling, PREPRINT (2016). [7] Schwarz, A.B., Trolle, E.S. Unspanned Stochastic Volatility and the Pricing of Com modity Derivatives, PREPRINT (2014).  

Gonzalez, Jhonny (U. Manchester)  Lecture Room 13  Thu, 7. Jul 16, 15:00 
"Bayesian Calibration and Number of Jump Components in Electricity Spot Price Models"  
The price spikes observed in electricity spot markets may be under stood to arise from fundamental drivers on both the supply and demand sides. Each driver can potentially create spikes with dierent frequencies, height dis tributions and rates of decay. This behaviour can be accounted for in models with multiple superposed components, however their calibration is challeng ing. Given a price history we apply a Markov Chain Monte Carlo (MCMC) based procedure to generate posterior samples from an augmented state space comprising parameters and multiple driving jump processes. This also enables posterior predictive checking to assess model adequacy. The procedure is used to determine the number of signed jump components required in two dierent markets, in time periods both before and after the recent global nancial crises. Joint work with John Moriarty and Jan Palczewski.  

Wunderlich, Ralf (TU Brandenburg)  Lecture Room 13  Thu, 7. Jul 16, 15:30 
"Partially Observable Stochastic Optimal Control Problems for an Energy Storage"  
We address the valuation of an energy storage facility in the pres ence of stochastic energy prices as it arises in the case of a hydroelectric pump station. The valuation problem is related to the problem of de termining the optimal charging/discharging strategy that maximizes the expected value of the resulting discounted cash ows over the life time of the storage. We use a regime switching model for the energy price which allows for a changing eco nomic environment described by a nonobservable Markov chain. The valuation problem is formulated as a stochastic control prob lem under partial informa tion in continuous time. Applying ltering theory we nd an alternative state process containing the lter of the Markov chain, which is adapted to the ob servable ltration. For this alternative control problem we derive the associated Hamilton JacobiBellman (HJB) equation which is not strictly elliptic. There fore we study the HJB equation using regularization arguments. We use nu merical methods for computing approximations of the value function and the optimal strategy. Finally, we present some numerical results. Joint work with Anton Shardin.  

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