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October  2015, 11(4): 1275-1283. doi: 10.3934/jimo.2015.11.1275

Portfolio optimization using a new probabilistic risk measure

Yufei Sun 1, , Grace Aw 1, , Kok Lay Teo 1, and  Guanglu Zhou 1,

1. 

Department of Mathematics and Statistics, Curtin University, Kent Street, Bentley, WA 6102, Australia, Australia, Australia, Australia

Received  February 2014 Revised  September 2014 Published  March 2015

In this paper, we introduce a new portfolio selection method. Our method is innovative and flexible. An explicit solution is obtained, and the selection method allows for investors with different degree of risk aversion. The portfolio selection problem is formulated as a bi-criteria optimization problem which maximizes the expected portfolio return and minimizes the maximum individual risk of the assets in the portfolio. The efficient frontier using our method is compared with various efficient frontiers in the literature and found to be superior to others in the mean-variance space.
Keywords: probabilistic risk measure., optimization, minimax, chance constraint, Portfolio selection.
Mathematics Subject Classification: 90C05, 90C20, 90C9.
Citation: Yufei Sun, Grace Aw, Kok Lay Teo, Guanglu Zhou. Portfolio optimization using a new probabilistic risk measure. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1275-1283. doi: 10.3934/jimo.2015.11.1275
References:
[1]

P. Artzner, F. Delbaen, J. M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance, 9 (1999), 203-228. doi: 10.1111/1467-9965.00068.

[2]

X. Q. Cai, K. L. Teo, X. Q. Yang and X. Y. Zhou, Portfolio optimization under a minimax rule, Management Science, 46 (2000), 957-972. doi: 10.1287/mnsc.46.7.957.12039.

[3]

X. T. Cui, S. S. Zhu, X. L. Sun and D. Li, Nonlinear portfolio selection using approximate parametric Value-at-Risk, Journal of Banking & Finance, 37 (2013), 2124-2139. doi: 10.1016/j.jbankfin.2013.01.036.

[4]

X. T. Deng, Z. F. Li and S. Y. Wang, A minimax portfolio selection strategy with equilibrium, European Journal of Operational Research, 166 (2005), 278-292. doi: 10.1016/j.ejor.2004.01.040.

[5]

H. Konno, Piecewise linear risk function and portfolio optimization, Journal of the Operations Research Society of Japan, 33 (1990), 139-156.

[6]

H. Konno and K. Suzuki, A mean-variance-skewness optimization model, Journal of the Operations Research Society of Japan, 38 (1995), 137-187.

[7]

H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science, 37 (1991), 519-531. doi: 10.1287/mnsc.37.5.519.

[8]

X. Li and Z. Y. Wu, Dynamic downside risk measure and optimal asset allocation,, Presented at FMA., (). 

[9]

P. C. Lin, Portfolio optimization and risk measurement based on non-dominated sorting genetic algorithm, Journal Of Industrial And Management Optimization, 8 (2012), 549-564. doi: 10.3934/jimo.2012.8.549.

[10]

H. Markowitz, Portfolio Selection, The Journal of Finance, 7 (1952), 77-91.

[11]

H. Markowitz, Portfolio Selection: Efficient Diversification of Investment, John Wiley & Sons, New York, 1959.

[12]

G. G. Polak, D. F. Rogers and D. J. Sweeney, Risk management strategies via minimax portfolio optimization, European Journal of Operational Research, 207 (2010), 409-419. doi: 10.1016/j.ejor.2010.04.025.

[13]

K. L. Teo and X. Q. Yang, Portfolio selection problem with minimax type risk function, Annals of Operations Research, 101 (2001), 333-349. doi: 10.1023/A:1010909632198.

[14]

T. L. Vincent and W. J. Grantham, Optimality in Parametric Systems, John Wiley & Sons, New York, 1981.

[15]

H. X. Yao, Z. F. Li and Y. Z. Lai, Mean-CVaR portfolio selection: A nonparametric estimation framework, Computers and Operations Research, 40 (2013), 1014-1022. doi: 10.1016/j.cor.2012.11.007.

show all references

References:
[1]

P. Artzner, F. Delbaen, J. M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance, 9 (1999), 203-228. doi: 10.1111/1467-9965.00068.

[2]

X. Q. Cai, K. L. Teo, X. Q. Yang and X. Y. Zhou, Portfolio optimization under a minimax rule, Management Science, 46 (2000), 957-972. doi: 10.1287/mnsc.46.7.957.12039.

[3]

X. T. Cui, S. S. Zhu, X. L. Sun and D. Li, Nonlinear portfolio selection using approximate parametric Value-at-Risk, Journal of Banking & Finance, 37 (2013), 2124-2139. doi: 10.1016/j.jbankfin.2013.01.036.

[4]

X. T. Deng, Z. F. Li and S. Y. Wang, A minimax portfolio selection strategy with equilibrium, European Journal of Operational Research, 166 (2005), 278-292. doi: 10.1016/j.ejor.2004.01.040.

[5]

H. Konno, Piecewise linear risk function and portfolio optimization, Journal of the Operations Research Society of Japan, 33 (1990), 139-156.

[6]

H. Konno and K. Suzuki, A mean-variance-skewness optimization model, Journal of the Operations Research Society of Japan, 38 (1995), 137-187.

[7]

H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science, 37 (1991), 519-531. doi: 10.1287/mnsc.37.5.519.

[8]

X. Li and Z. Y. Wu, Dynamic downside risk measure and optimal asset allocation,, Presented at FMA., (). 

[9]

P. C. Lin, Portfolio optimization and risk measurement based on non-dominated sorting genetic algorithm, Journal Of Industrial And Management Optimization, 8 (2012), 549-564. doi: 10.3934/jimo.2012.8.549.

[10]

H. Markowitz, Portfolio Selection, The Journal of Finance, 7 (1952), 77-91.

[11]

H. Markowitz, Portfolio Selection: Efficient Diversification of Investment, John Wiley & Sons, New York, 1959.

[12]

G. G. Polak, D. F. Rogers and D. J. Sweeney, Risk management strategies via minimax portfolio optimization, European Journal of Operational Research, 207 (2010), 409-419. doi: 10.1016/j.ejor.2010.04.025.

[13]

K. L. Teo and X. Q. Yang, Portfolio selection problem with minimax type risk function, Annals of Operations Research, 101 (2001), 333-349. doi: 10.1023/A:1010909632198.

[14]

T. L. Vincent and W. J. Grantham, Optimality in Parametric Systems, John Wiley & Sons, New York, 1981.

[15]

H. X. Yao, Z. F. Li and Y. Z. Lai, Mean-CVaR portfolio selection: A nonparametric estimation framework, Computers and Operations Research, 40 (2013), 1014-1022. doi: 10.1016/j.cor.2012.11.007.

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