Objective comparisons of the optimal portfolios corresponding to different utility functions
This paper considers the effects of some frequently used utility functions in portfolio selection by comparing the optimal investment outcomes corresponding to these utility functions. Assets are assumed to form a complete market of the Black-Scholes type. Under consideration are four frequently used utility functions: the power, logarithm, exponential and quadratic utility functions. To make objective comparisons, the optimal terminal wealths are derived by integration representation. The optimal strategies which yield optimal values are obtained by the integration representation of a Brownian martingale. The explicit strategy for the quadratic utility function is new. The strategies for other utility functions such as the power and the logarithm utility functions obtained this way coincide with known results obtained from Merton's dynamic programming approach.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
- Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
- Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2009. "Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm," European Journal of Operational Research, Elsevier, vol. 192(2), pages 603-620, January.
- Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 337-356.
- Ballestero, E. & Gunther, M. & Pla-Santamaria, D. & Stummer, C., 2007. "Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1476-1487, September.
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Buckley, Ian & Saunders, David & Seco, Luis, 2008. "Portfolio optimization when asset returns have the Gaussian mixture distribution," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1434-1461, March.
- Zhao, Yonggan, 2007. "A dynamic model of active portfolio management with benchmark orientation," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3336-3356, November.
- Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
- Zhang, Wei-Guo & Zhang, Xi-Li & Xiao, Wei-Lin, 2009. "Portfolio selection under possibilistic mean-variance utility and a SMO algorithm," European Journal of Operational Research, Elsevier, vol. 197(2), pages 693-700, September.
- Rambaud, Salvador Cruz & Pérez, José García & Sánchez Granero, Miguel Ángel & Trinidad Segovia, Juan Evangelista, 2009. "Markowitz's model with Euclidean vector spaces," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1245-1248, August.
- Nepal, Bimal & Lassan, Gregg & Drow, Baba & Chelst, Kenneth, 2009. "A set-covering model for optimizing selection of portfolio of microcontrollers in an automotive supplier company," European Journal of Operational Research, Elsevier, vol. 193(1), pages 272-281, February.
- Shen, Ruijun & Zhang, Shuzhong, 2008. "Robust portfolio selection based on a multi-stage scenario tree," European Journal of Operational Research, Elsevier, vol. 191(3), pages 864-887, December.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
- de Palma, André & Prigent, Jean-Luc, 2008. "Utilitarianism and fairness in portfolio positioning," Journal of Banking & Finance, Elsevier, vol. 32(8), pages 1648-1660, August.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
- Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
- Paris, Francesco M., 2005. "Selecting an optimal portfolio of consumer loans by applying the state preference approach," European Journal of Operational Research, Elsevier, vol. 163(1), pages 230-241, May.
- Charles D. Feinstein & Mukund N. Thapa, 1993. "Notes: A Reformulation of a Mean-Absolute Deviation Portfolio Optimization Model," Management Science, INFORMS, vol. 39(12), pages 1552-1553, December. Full references (including those not matched with items on IDEAS)