Portfolio selection in stochastic markets with exponential utility functions

• Published in: Annals of operations research 2009-02, Vol.166 (1), p.281-297
• Main Authors: Çanakoğlu, Ethem, Özekici, Süleyman
• Format: Article
• Language: English
• Subjects: Business and Management; Combinatorics; Dynamic programming; Expected utility; Fourier transforms; Investments; Investors; Markov analysis; Operations research; Operations Research/Decision Theory; Optimization; Portfolio investments; Portfolio management; Rates of return; Studies; Theory of Computation; Utility functions
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-008-0406-2

We consider the optimal portfolio selection problem in a multiple period setting where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has an exponential structure and the market states change according to a Markov chain. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. The problem is solved using the dynamic programming approach to obtain the optimal solution and an explicit characterization of the optimal policy. We also discuss the stochastic structure of the wealth process under the optimal policy and determine various quantities of interest including its Fourier transform. The exponential return-risk frontier of the terminal wealth is shown to have a linear form. Special cases of multivariate normal and exponential returns are disussed together with a numerical illustration.