Optimal Stopping and the American Option with Hereditary Price Structures

Dr. Mou-Hsiung Chang

Department of Mathematical Sciences
University of Alabama in Huntsville

October 9, 1998

Abstract

This talk is based on a joint paper with Dr. Roger Youree entitled "The American Option with hereditary Price Structures: Generalized HJB Variational Inequality." In this talk we consider a new model for the (B,S)-market in which the stock price and the asset in the riskless bank account have hereditary price structures. Specifically, the dynamics of the stock price and the bank account are described by linear stochastic functional differential equations. The pricing of the American contingent claims is studied and the corresponding trading strategy is derived. We also prove that the pricing function of the American option is a viscosity solution of a generalized Hamilton-Jocobi-Bellman variational inequality.