Financial/Actuarial Mathematics Seminar

Academic Year 2006-2007: Thursdays 3:10-4:00, 3088 East Hall

Computational Parameter Optimization and Differential Equations For Stock Markets

Ahmet Duran

Department of Mathematics, University of Michigan

September 21, 2006

Abstract
We combine an implementation of a state-of-the-art optimization algorithm and a system of nonlinear differential equations to describe price dynamics. Given an n-day period of market price (MP) and net asset value (NAV) from day i to day i+n-1, we obtain four optimal parameters in the differential equations derived by Caginalp by using a nonlinear computational optimization technique. We then solve the initial value problem to predict MP and return on day i+n or later. We provide out-of-sample prediction that is more successful than random walk.

Abstract

We combine an implementation of a state-of-the-art optimization algorithm and a system of nonlinear differential equations to describe price dynamics. Given an n-day period of market price (MP) and net asset value (NAV) from day i to day i+n-1, we obtain four optimal parameters in the differential equations derived by Caginalp by using a nonlinear computational optimization technique. We then solve the initial value problem to predict MP and return on day i+n or later. We provide out-of-sample prediction that is more successful than random walk.

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