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

Objective comparisons of the optimal portfolios corresponding to different utility functions. (English) Zbl 1176.90637

Eur. J. Oper. Res. 199, No. 2, 604-610 (2009).
Summary: 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.

Cited in 7 Documents

MSC:

90C46 Optimality conditions and duality in mathematical programming
91G10 Portfolio theory

Keywords:

utility function; optimal portfolio; martingale measure; integration representation; Brownian martingales
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[1] Bálbas, A.; Bálbas, R.; Mayoral, S., Portfolio choice and optimal hedging with general risk functions: a simplex-like algorithm, European Journal of Operational Research, 192, 2, 603-620 (2009) · Zbl 1157.91350
[2] Ballestero, E.; Günther, M.; Pla-Santamaria, D.; Stummer, C., Portfolio selection under strict uncertainty: a multi-criteria methodology and its application to the Frankfurt and Vienna stock exchanges, European Journal of Operational Research, 181, 3, 1476-1487 (2007) · Zbl 1123.91022
[3] Ben-Tal, A.; Nemirovski, A., Robust convex optimization, Mathematics of Operations Research, 23, 769-805 (1998) · Zbl 0977.90052
[4] Ben-Tal, A.; Nemirovski, A., Robust solution of uncertain linear programs, Operations Research, 25, 1-38 (1999) · Zbl 0941.90053
[5] Black, F.; Scholes, M., The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637-659 (1973) · Zbl 1092.91524
[6] Browne, S., Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 20, 4, 937-958 (1995) · Zbl 0846.90012
[7] Buckley, I.; Saunders, D.; Seco, L., Portfolio optimization when asset returns have the Gaussian mixture distribution, European Journal of Operational Research, 185, 3, 1434-1461 (2008) · Zbl 1149.90084
[8] Cai, X.; Teo, K. L.; Zhou, X. Y., Portfolio optimization under a minimax rule, Management Science, 46, 7, 957-972 (2000) · Zbl 1231.91149
[9] Cox, J.; Huang, C. F., Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory, 49, 33-83 (1989) · Zbl 0678.90011
[10] Cruz Rambaud, S.; Pérez, J. G.; Granero, M. A.S.; Segovia, J. E.T., Markowitzs model with Euclidean vector spaces, European Journal of Operational Research, 196, 3, 1245-1248 (2009) · Zbl 1176.91061
[11] Davies, R.J., Kat, H.M., Lu, S., 2004. Fund of Hedge Funds Portfolio Selection: A Multiple-Objective Approach. Working Paper, ISMA Centre, University of Reading, UK.; Davies, R.J., Kat, H.M., Lu, S., 2004. Fund of Hedge Funds Portfolio Selection: A Multiple-Objective Approach. Working Paper, ISMA Centre, University of Reading, UK.
[12] Duffie, D., 1996. Dynamic Asset Pricing Theory. Princeton.; Duffie, D., 1996. Dynamic Asset Pricing Theory. Princeton. · Zbl 1140.91041
[13] Fei, W., Optimal consumption and portfolio choice with ambiguity and anticipation, Information Sciences, 177, 23, 5178-5190 (2007) · Zbl 1305.91216
[14] Feinstein, C. D.; Thapa, M. N., Notes: a reformulation of a mean-absolute deviation portfolio optimization model, Management Science, 39, 12, 1552-1553 (1993) · Zbl 0796.90002
[15] Gaivoronski, A. A.; Krylov, S.; Wijst, Nico van der, Optimal portfolio selection and dynamic benchmark tracking, European Journal of Operational Research, 163, 1, 115-131 (2005) · Zbl 1066.91040
[16] Huang, C. F.; Litzenberger, Foundations For Financial Economics (1988), Prentice Hall: Prentice Hall New Jersey · Zbl 0677.90001
[17] Ingersoll, J. E., Theory of Financial Decision Making (1987), MD: MD Rowman & Littlefield
[18] Jiao, J.; Zhang, Y.; Wang, Y., A heuristic genetic algorithm for product portfolio planning, Computers and Operations Research, 34, 6, 1777-1799 (2007) · Zbl 1159.90371
[19] Josa-Fombellida, R.; Pablo, J.; Zapatero, Rincón., Mean-variance portfolio and contribution selection in stochastic pension funding, European Journal of Operational Research, 187, 1, 120-137 (2008) · Zbl 1135.91019
[20] Karatzas, I., Optimization problems in the theory of continuous trading, SIAM Journal of Control and Optimization, 7, 1221-1259 (1989) · Zbl 0701.90008
[21] Karatzas, I.; Lehoczky, J. P.; Shreve, S. E., Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM Journal of Control and Optimization, 25, 1157-1186 (1987)
[22] Karatzas, I.; Shreve, S. E., Brownian Motion and Stochastic Calculus (1991), Springer · Zbl 0734.60060
[23] Konno, H., Piecewise linear risk function and portfolio optimization, Journal of the Operational Research Society Japan, 33, 139-156 (1990) · Zbl 0706.90005
[24] Konno, H.; Yamazaki, H., Mean-absolute deviation portfolio optimization model and its applications to tokyo stock market, Management Science, 37, 5, 519-531 (1991)
[25] Markowitz, H., Portfolio selection, Journal of Finance, 7, 1, 77-91 (1952)
[26] Merton, R. C., Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3, 373-413 (1971) · Zbl 1011.91502
[27] Merton, R. C., Continuous-Time Finance (1990), Blackwell: Blackwell Cambridge, MA
[28] Morton, A. J.; Pliska, S. R., Optimal portfolio management with fixed transaction costs, Mathematical Finance, 5, 337-356 (1995) · Zbl 0866.90020
[29] Nepal, B.; Lassan, G.; Drow, B.; Chelst, K., A set-covering model for optimizing selection of portfolio of microcontrollers in an automotive supplier company, European Journal of Operational Research, 193, 1, 272-281 (2009) · Zbl 1152.90678
[30] Palma, A.; Prigent, J. L., Utilitarianism and fairness in portfolio positioning, Journal of Banking and Finance, 32, 8, 1648-1660 (2008)
[31] Paris, F. M., Selecting an optimal portfolio of consumer loans by applying the state preference approach, European Journal of Operational Research, 163, 1, 230-241 (2005) · Zbl 1067.90083
[32] Pliska, S. R., A stochastic calculus model of continuous trading: optimal portfolios, Mathematics of Operations Research, 11, 371-382 (1986) · Zbl 1011.91503
[33] Pratt, J., Risk aversion in the small and in the large, Econometrica, 32, 122-130 (1964) · Zbl 0132.13906
[34] Ross, M. S., An Elementary Introduction To Mathematical Finance (2003), Cambridge University Press · Zbl 1113.91025
[35] Shen, R.; Zhang, S., Robust portfolio selection based on a multi-stage scenario tree, European Journal of Operational Research, 191, 3, 864-887 (2008) · Zbl 1157.91014
[36] Thorp, E. O., Portfolio choice and the Kelly criterion, (Ziemba, W. T.; Vickson, R. G., Stochastic Optimization Models in Finance (1975), Academic Press: Academic Press New York) · Zbl 0119.31904
[37] Yu, L.; Wang, S.; Lai, K. K., Neural network-based mean-variance Vskewness model for portfolio selection, Computers and Operations Research, 35, 1, 34-46 (2008) · Zbl 1139.91347
[38] Zhang, W. G.; Zhang, X. L.; Xiao, W. L., Portfolio selection under possibilistic mean-variance utility and a SMO algorithm, European Journal of Operational Research, 197, 2, 693-700 (2009) · Zbl 1159.90471
[39] Zhao, Y., A dynamic model of active portfolio management with benchmark orientation, Journal of Banking and Finance, 31, 11, 3336-3356 (2007)
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