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Objective comparisons of the optimal portfolios corresponding to different utility functions

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  • Yu, Bosco Wing-Tong
  • Pang, Wan Kai
  • Troutt, Marvin D.
  • Hou, Shui Hung

Abstract

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.

Suggested Citation

  • Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
  • Handle: RePEc:eee:ejores:v:199:y:2009:i:2:p:604-610
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    1. 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.
    2. 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.
    3. Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 337-356.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
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    Cited by:

    1. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2015. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability," European Journal of Operational Research, Elsevier, vol. 246(2), pages 528-542.
    2. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2013. "On the equivalence of quadratic optimization problems commonly used in portfolio theory," European Journal of Operational Research, Elsevier, vol. 229(3), pages 637-644.
    3. Ben Ameur, H. & Prigent, J.L., 2014. "Portfolio insurance: Gap risk under conditional multiples," European Journal of Operational Research, Elsevier, vol. 236(1), pages 238-253.
    4. Ni, Jian & Chu, Lap Keung & Wu, Feng & Sculli, Domenic & Shi, Yuan, 2012. "A multi-stage financial hedging approach for the procurement of manufacturing materials," European Journal of Operational Research, Elsevier, vol. 221(2), pages 424-431.
    5. Chang, Ching-Ter, 2011. "Multi-choice goal programming with utility functions," European Journal of Operational Research, Elsevier, vol. 215(2), pages 439-445, December.
    6. Fulga, Cristinca, 2016. "Portfolio optimization with disutility-based risk measure," European Journal of Operational Research, Elsevier, vol. 251(2), pages 541-553.

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