APPLICATIONS OF OPTIMAL CONTROL AND STOCHASTIC REPRESENTATION IN FINANCIAL MODELING

Abstract

This thesis contains two parts. In Part I, we develop an optimal tax-timing model that takes into account the asymmetric tax rates structure on capital gains and limited tax deductibility of capital losses. This model can help explain why many investors not only defer short-term capital losses to long term but also defer large long-term capital gains and losses. We also find that effective tax rates can decrease as the short-term capital gains tax rates increase. In Part II we study the valuation of dual-purpose funds in China. We provide a mathematical formulation of the fund contract, and discuss its pricing under the Black-Scholes framework. Motivated by the fund valuation, we establish a stochastic representation for solutions to parabolic PDEs with nonlocal terminal and boundary conditions, in terms of a space-time diffusion process that jumps at the domain boundary. This representation result gives a PDE characterization of the fund value.