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Title: Optimal stopping problems with applications to finance
Author: Chun, Wang
ISNI:       0000 0004 2742 5543
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2012
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This thesis considers several optimal stopping problems motivated by mathematical fi- nance, using the so-called martingale and Markov approaches for optimal stopping prob- lems. We first extend the pricing problem for American options under geometric Brownian motion models to a wider range of payoff functions and, by adding a continuous-time Markov chain to the dynamic, to a regime-switching model. We then allow the time horizon during which the underlying process evolves to be a random variable. This is further adapted to a regime-switching Cox-Ingersoll-Ross model with application to pricing American bond options. The key idea for all these three extensions is to simplify the problems by removing their dependence on the Markov chain and so reducing them to the study of simplified optimal stopping problems for which the martingale approach works. We then compose the value functions of the latter problems in certain manner to obtain the solutions of the original problems. We obtain the shape of optimal stopping regions and the differential equations satisfied by the value functions. Another problem we consider is an optimal prediction problem for Geometric Brownian motion which is motivated by selling stocks at optimal prices. We use the Girsanov theory of change of measure to transform the prediction problem to a standard optimal stopping problem with a reflected Brownian motion as the underlying process. We then follow the Markov approach to investigate the shape of the stopping region and characterize the optimal selling rule for the original problem.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available