The Optimal expected Utility Variance Problem

Specialeforsvar ved Nooshin Aminpour Majoormardi

Titel: The Optimal Expected Utility Variance Problem

Abstract: In this thesis we analyse three different portfolio optimization problems in continuous time. We start by considering two well-known optimization problems, the expected utility problem and the mean-variance problem. Inspired by these we make our own optimization problem which uses the punishment on the variance from the mean-variance problem and the utility function from the expected utility problem. The new optimization problem is called the expected utility variance problem, and we analyse how this problem compares to the other problems. The problems are analysed in a Black-Scholes market, and we use the martingale method in order to find the solutions to our optimization problems. For the expected utility problem and the mean-variance problem we find explicit solutions, and for the expected utility variance problem we find a numerical solution. We compare the methods by looking at plots which among other things illustrate the development of the optimal portfolios and the corresponding optimal wealth. In addition we use the efficient frontier, in order to get a fuller picture. 

Vejleder: Jesper Lund Pedersen
Censor:   Bjarne Astrup Jensen, CBS