Convex Stochastic Control and Conjugate Duality in a Problem of Unconstrained Utility Maximization Under a Regime Switching Model

utility optimization;regime switching model;conjugate duality;stochastic calculus;convex stochastic control;mathematical finance;Quantitative Finance

Situ, Aaron Xin

University of Waterloo

关键词: utility optimization;    regime switching model;    conjugate duality;    stochastic calculus;    convex stochastic control;    mathematical finance;    Quantitative Finance;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/9389/5/Situ_AaronXin.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, we examine a problem of convex stochastic optimal control applied to mathematicalfinance. The goal is to maximize the expected utility from wealth at close of trade (or terminal wealth)under a regime switching model. The presence of regime switching constitutes a definite challenge, andin order to keep the analysis tractable we therefore adopt a market model which is in other respects quitesimple, and in particular does not involve margin payments, inter-temporal consumption or portfolioconstraints. The asset prices will be modeled by classical Ito processes, and the market parameterswill be dependent on the underlying Brownian Motion as well as a finite-state Markov Chain whichrepresents the ;;regime switching;; aspect of the market model. We use conjugate duality to constructa dual optimization problem and establish optimality relations between (putative) solutions of the dualand primal problems. We then apply these optimality relations to two specific types of utility functions,namely the power utility and logarithmic utility functions, and for these utility functions we obtain theoptimal portfolios in completely explicit and implementable form.