## Wolfgang Pauli Institute (WPI) Vienna

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## Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance"

 Location: WPI Seminar Room C714 Fri, 22. Jun (Opening: 9:00) - Sat, 23. Jun 12
Topics:
Many problems in finance can be posed as non-linear Hamilton Jacobi Bellman (HJB) Partial Integro Differential Equations (PIDEs). Examples of such problems include: dynamic asset allocation for pension plans, optimal operation of natural gas storage facilities, optimal execution of trades, and pricing of variable annuity products. (e.g. Guaranteed Minimum Withdrawal Benefit). This course will discuss general numerical methods for solving the HJB PDEs which arise from these types of problems. After an introductory lecture, we will give an example where seemingly reasonable methods do not Course highlights: Day 1: (e.g. Guaranteed Minimum Withdrawal Benefit).
 Organisation(s) WPI Organiser(s) Peter Laurence (U. Roma) RenĂ© Aid (Electricite' de France) Fred Benth (U. Oslo) Valery Kholodnyi (Verbund) Almut Veraart (Imperial College)
 Remark: Speaker: Professor Peter Forsyth, University of Waterloo Mathematical Models for the commodity markets (Numerical methods for Hamilton-Jacobi equations in finance)
Many problems in finance can be posed as non-linear Hamilton Jacobi Bellman (HJB) Partial Integro Differential Equations (PIDEs). Examples of such problems include: dynamic asset allocation for pension plans, optimal operation of natural gas storage facilities, optimal execution of trades, and pricing of variable annuity products. (e.g. Guaranteed Minimum Withdrawal Benefit). This course will discuss general numerical methods for solving the HJB PDEs which arise from these types of problems. After an introductory lecture, we will give an example where seemingly reasonable methods do not Course highlights: Day 1: (e.g. Guaranteed Minimum Withdrawal Benefit).

This course will include:

Day 1
Lecture 1: Examples of HJB Equations, Viscosity Solutions (1 hour)
Lecture 2: Sufficient Conditions for Convergence to the Viscosity Solution (1 hour)
Lecture 3: Pension Plan Asset Allocation, Passport Options (1 hr)
Lecture 4: Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity: Impulse Control Formulation (1 hr)
Lecture 5: Gas Storage (1 hr)

Day 2:
Lecture 6: Continuous Time Mean Variance Asset Allocation (1 hr)
Lecture 7: Optimal Trade Execution (1 hr)
Lecture 8: Summary (.5 hr)

### Talks in the framework of this event

 Peter Forsyth WPI, Seminarroom C 714 Fri, 22. Jun 12, 10:00 Examples of HJB Equations, Viscosity Solutions Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Fri, 22. Jun 12, 11:00 Sufficient Conditions for Convergence to the Viscosity Solution Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Fri, 22. Jun 12, 14:00 Pension Plan Asset Allocation, Passport Options Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Fri, 22. Jun 12, 15:00 Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity: Impulse Control Formulation Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Fri, 22. Jun 12, 16:00 Gas Storage Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Sat, 23. Jun 12, 10:00 Continuous Time Mean Variance Asset Allocation Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Sat, 23. Jun 12, 11:00 Optimal Trade Execution Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)

 Peter Forsyth WPI, Seminarroom C 714 Sat, 23. Jun 12, 12:00 Summary Mini-Course Thematic program: Mathematical-finance: Applications to Energy Markets, Risc Management and Pricing of Derivatives (2012) Event: Mini-Course: "Numerical methods for Hamilton-Jacobi equations in mathematical finance" (2012)