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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.

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  • 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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    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. 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.
    4. Ruili Sun & Tiefeng Ma & Shuangzhe Liu, 2018. "A Stein-type shrinkage estimator of the covariance matrix for portfolio selections," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 931-952, November.
    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. Gatzert, Nadine & Martin, Alexander & Schmidt, Martin & Seith, Benjamin & Vogl, Nikolai, 2021. "Portfolio optimization with irreversible long-term investments in renewable energy under policy risk: A mixed-integer multistage stochastic model and a moving-horizon approach," European Journal of Operational Research, Elsevier, vol. 290(2), pages 734-748.
    7. Fulga, Cristinca, 2016. "Portfolio optimization with disutility-based risk measure," European Journal of Operational Research, Elsevier, vol. 251(2), pages 541-553.
    8. 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.

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