Optimal decisions in finance: passport options and the bonus problem

Thesis

The object of this thesis is the study of some new financial models. The common feature is that they all involve optimal decisions. Some of the decisions take the form of a control and we enter the theory of stochastic optimal control and of Hamilton-Jacobi-Bellman (HJB) equations. Other decisions are "binary" and we deal with the theory of optimal stopping and free boundary problems.

Throughout the thesis we will prefer a heuristic and intuitive approach to a too technical one which could hide the underlying ideas.

In the first part we introduce the reader to option pricing, HJB equations and free boundary problems, and we review briefly the use of these mathematical tools in finance.

The second part of the thesis deals with passport options. The pricing of these exotic options involves stochastic optimal control and free boundary problems. Finally, in the last part we study the end-of-the-year bonus for traders: how to optimally reward a trader?

Authors: Penaud, A

• Publication date: 2000
• DOI: 10.5287/ora-dqmgwxvnr
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: passport options; stochastic optimal control; bonus
• Subjects: Mathematical finance