Date of Award

May 2013

Degree Type

Thesis

Degree Name

Master of Science

Department

Mathematics

First Advisor

Chao Zhu

Committee Members

Richard Stockbridge, Eric Key

Keywords

Girsanov Theorem, Hjbi Equation, Risk Indifference Pricing, Risk Measures, Viscosity Solutions

Abstract

This paper is concerned with risk indifference pricing of a European type contingent claim in an incomplete market, where the evolution of the price of the underlying stock is modeled by a regime-switching jump diffusion. The rationale of using such a model is that it can naturally capture the inherent randomness of a prototypical stock market by incorporating both small and big jumps of the prices as well as the qualitative changes of the market. While the model provides a realistic description of the real market, it does introduces substantial difficulty in the analysis. In particular, in contrast with the classical Black-Scholes model, there are infinitely many equivalent martingale measures and hence the price is not unique in our incomplete market. In particular, there exists a big gap between the commonly used sub- and super-hedging prices.\\

We approach this problem using the framework of risk-indifference pricing. By transforming the pricing problem to an equivalent stochastic game problem, we solve this problem via the associated Hamilton-Jacobi-Bellman-Issac equations. Consequently we obtain a new interval which is smaller than the interval from super- and sub-hedging.

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