Talks by Dr. Wan: "Talk 3: Numerical Methods for PDE Problems arising from Option Pricing, Asset Allocation, and Dynamic Bertrand Oligopolies"
August 1st (Tuesday), 11:00-12:00 am
National Institute of Informatics
Room: 19F, 1901
Numerical Methods for PDE Problems arising from Option Pricing, Asset Allocation, and Dynamic Bertrand Oligopolies
Dr. Justin W.L. Wan
Canada Research Chair in Scientific Computing,
Associate Professor, SciCom group in the David R. Cheriton School of Computer Science at University of Waterloo, Canada,
Director of the Centre for Computational Mathematics in Industry and Commerce (CCMIC).
Black-Scholes modeling is central in computational finance. It also leads to PDEs with challenging numerical issues. In this talk, we will present accurate and efficient numerical methods for solving different types of PDEs that arise from option pricing, asset allocation, regime switching and Bertrand oligopolies. In particular, we present an accurate finite difference method for solving partial integro-differential equations arising from pricing European and American options when the underlying asset is driven by a CGMY process. We will then present numerical methods and fast solvers for solving Hamilton-Jacobi-Bellman (HJB) equations as well as the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, which arise in asset allocation and stochastic optimal control problems. When there are multiple value functions, for instance, regime switching models in option pricing, or nonzero sum stochastic differential games in dynamic Bertrand oligopoly, the resulting model will result in a system of coupled HJB PDEs. We will discuss the discretization of the nonlinear systems, the issues of viscosity solutions, monotone finite difference schemes, and fast solvers for solving the systems of discrete HJB equations. We demonstrate numerically the performance of the numerical methods by examples of various computational finance problems.
Ken Hayami (hayami(at)nii.ac.jp)