Law, S. L. (2005) Financial optimization problems. PhD thesis, University of Oxford.

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Abstract
The major objective of this thesis is to study optimization problems in finance. Most of the effort is directed towards studying the impact of transaction costs in those problems. In addition, we study dynamic meanvariance asset allocation problems. Stochastic HJB equations, Pontryagin Maximum Principle and perturbation analysis are the major mathematical techniques used.
In Chapter 1, we introduce the background literature. Following that, we use the Pontryagin Maximum Principle to tackle the problem of dynamic meanvariance asset allocation and rediscover the doubling strategy. In Chapter 2, we present one of the major results of this thesis. In this chapter, we study a financial optimization problem based on a market model without transaction costs first. Then we study the equivalent problem based on a market model with transaction costs. We find that there is a relationship between these two solutions. Using this relationship, we can obtain the solution of one when we have the solution of another.
In Chapter 3, we generalize the results of chapter 2.
In Chapter 4, we use Pontryagin Maximum Principle to study the problem limit of the notransaction region when transaction costs tend to 0. We find that the limit is the notransaction cost solution.
Item Type:  Thesis (PhD) 

Subjects:  D  G > Game theory, mathematical finance, economics, social and behavioral sciences 
Research Groups:  Mathematical and Computational Finance Group 
ID Code:  240 
Deposited By:  Eprints Administrator 
Deposited On:  23 Jun 2006 
Last Modified:  29 May 2015 18:18 
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