Graduation Semester and Year

2013

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Andrzej Korzeniowski

Abstract

Despite the outstanding success of the Black-Scholes model, it relies on the assumption that drift and volatility of the underlying equity remain constant throughout time. This inaccuracy has motivated a number of interesting and innovative refinements, one of the most natural being Markov modulation. In this dissertation we analyze a variety of financially motivated optimal stopping problems under Markov modulated Ito-Diffusions. In Chapter 3, we generalize and refine a technique developed in [13] pricing an infinite time horizon American put option and we present a rigorous proof of optimality. In Chapter 3 we use this generalized technique to discover an optimal selling strategy for an infinite horizon American style forward contract. In so doing, we extend the work done in [12]. Finally in Chapter 5 we price the infinite horizon American put using a non-traditional model of a mean reverting Ornstein-Uhlenbeck process, further illustrating the broad scope of applicability of the technique developed herein.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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Included in

Mathematics Commons

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