The valuation of a gas storage facility is characterized as a stochastic control problem, result-... more The valuation of a gas storage facility is characterized as a stochastic control problem, result- ing in a Hamilton-Jacobi-Bellman (HJB) equation. In this paper, we present a semi-Lagrangian method for solving the HJB equation for a typical gas storage valuation problem. The method is able to handle a wide class of spot price models that exhibit mean-reverting, seasonality dy- namics and price jumps. We develop fully implicit and Crank-Nicolson timestepping schemes based on a semi-Lagrangian approach and prove the convergence of fully implicit timestepping to the viscosity solution of the HJB equation. We show that fully implicit timestepping is equiv- alent to a discrete control strategy, which allows for a convenient interpretation of the optimal controls. The semi-Lagrangian approach avoids the nonlinear iterations required by an implicit finite dierence
IMA Journal of Numerical Analysis (2005) 25, 87–112 doi:10.1093/imanum/drh011 ... Robust numerica... more IMA Journal of Numerical Analysis (2005) 25, 87–112 doi:10.1093/imanum/drh011 ... Robust numerical methods for contingent claims under jump diffusion processes ... Y. D 'H ALLUIN † AND PA F ORSYTH ‡ ... School of Computer Science, University of Waterloo, Waterloo ...
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Papers by Peter Forsyth