Numerical Methods for Linear and Nonlinear Problems in Computational Finance and Economics

Speaker: Justin Wan

Affiliation: University of Waterloo

In this talk, we will present accurate and efficient numerical methods for solving linear and nonlinear problems in the areas of computational finance and economics which give rise to interesting PDEs that show similarity to traditional PDE problems but also possess unique characteristics of its own. For instance, option pricing based on the standard Black-Scholes model leads to a heat equation, convection dominated problem, and a linear complementarity problem for the European, Asian, and American option, respectively. The jump-diffusion model which captures jumps in asset prices yields a partial integro-differential equation (PIDE). Recently, the more sophisticated financial models were formulated as optimal stochastic control problems which can be written as nonlinear Hamilton-Jacobi-Bellman equations (one control) and Hamilton-Jacobi-Bellman-Issac equations (two controls). These nonstandard PDEs give rise to new challenges to designing fast solvers.

In this talk, we will present accurate and efficient numerical methods for solving linear and nonlinear equations in finance and economics. We will also present theoretical analysis to justify the numerical techniques. Numerical results will be given for a variety of equations arising from financial and economic modeling.