Graduate School Dissertation Defense Information
Stochastic Systems Seminar
Abstract: We will show that symbolic computing systems are capable of transforming Feynman-type integrals on the pathspace into powerful numerical procedures for solving general partial differential equations of parabolic or elliptic type, inculding optimal control problems, which can be formulated as free-boundary problems. Compared to the widely used finite difference methods, such procedures are more universal and more robust to discontinuities in the boundary conditions. Numerical procedures based on path-integration are surprisingly easy to implement, and do not require any manipulation of the PDE. This is an ongoing research and rigorous estimates for the rate of convergence are yet to be established. We will illustrate the method with specific examples, mostly from computational finance. An economist or a financial engineer who works with very general models for asset valuation, including the so called stochastic volatility models, will find that this method is just as easy to work with as the classical Black;SCScholes model, in which asset values can follow only a geometric Brownian motion process.
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