Prospect theory-based formulation of chance constrained portfolio optimization problem using loan

Abstract

Portfolio optimization that allows the borrowed money from a loan to be invested in risk assets has been formulated as a chance constrained problem. In this paper, in order to reflect investor preferences called “values” in the solution, or the portfolio, prospect theory is used to expand the chance constrained problem that maximizes the profit. The new portfolio optimization problem maximizes the value instead of the profit. In order to get a deeper understanding of the characteristics of the new portfolio optimization problem, the fitness landscape analysis method using Convex-Hull Mapping (CHM) is employed. Furthermore, since the new portfolio optimization problem is usually non-convex, the multi-start local search method with CHM is used to find the solution. Finally, numerical experiments on artificial and actual asset data sets show that the solution of the new portfolio optimization problem is more acceptable to investors than the solution of the conventional one.

Keywords

• portfolio optimization problem
• chance constrained problem
• optimization method
• constraint-handling
• prospect theory