A fuzzy portfolio selection model with background risk. (English) Zbl 1338.91130
Summary: In financial markets, the presence of background risk may affect investors’ investments. This article develops a fuzzy portfolio selection model with background risk, based on the definitions of the possibilistic return and possibilistic risk. For the returns of assets obey LR-type possibility distribution, we propose a specific portfolio selection model with background risk. Then, a numerical study is carried out by using the data concerning some stocks. Based on the data, we obtain the efficient frontier of the possibilistic portfolio with background risk, and compare it with the efficient frontier of the portfolio without background risk. Finally, we conclude that the background risk can better reflect the investment risk of the real economy environment which make the investors choose a more suitable portfolio to them.
MSC:
| 91G10 | Portfolio theory |
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
References:
| [1] | Markowitz, H., Portfolio selection, J. Finance, 7, 77-91 (1952) |
| [2] | Sharpe, W. F., Portfolio Theory and Capital Markets (1970), McGraw-Hill: McGraw-Hill New York |
| [3] | Merton, R. C., An analytic derivation of the efficient portfolio frontier, J. Finance Quant. Anal., 7, 1851-1872 (1972) |
| [4] | Perold, A. F., Large-scale portfolio optimization, Manage. Sci., 30, 1143-1160 (1984) · Zbl 0548.90008 |
| [5] | Pang, J. S., A new and efficient algorithm for a class of portfolio selection problems, Oper. Res., 28, 754-767 (1980) · Zbl 0451.90011 |
| [6] | Zmeškal, Z., Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach), Int. Rev. Financial Anal., 14, 263-275 (2005) |
| [7] | Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1, 3-28 (1978) · Zbl 0377.04002 |
| [8] | Dubois, D.; Prade, H., Possibility Theory (1988), Plenum Press: Plenum Press New York · Zbl 0645.68108 |
| [9] | Carlsson, C.; Fullér, R.; Majlender, P., A possibilistic approach to selecting portfolios with highest utility score, Fuzzy Sets Syst., 131, 13-21 (2002) · Zbl 1027.91038 |
| [10] | Carlsson, C.; Fullér, R., Possibility for Decision: A Possibilistic Approach to Real Life Decisions (2011), Springer-Verlag: Springer-Verlag Berlin · Zbl 1227.91002 |
| [11] | Georgescu, I., Possibility Theory and The Risk (2012), Springer-Verlag: Springer-Verlag Berlin · Zbl 1239.91002 |
| [12] | Inuiguchi, M.; Tanino, T., Portfolio selection under independent possibilistic information, Fuzzy Sets Syst., 115, 83-92 (2000) · Zbl 0982.91028 |
| [13] | Zhang, W. G., Possibilistic mean-standard deviation models to portfolio selection for bounded assets, Appl. Math. Comput., 189, 1614-1623 (2007) · Zbl 1243.91097 |
| [14] | Zhang, W. G.; Wang, Y. L.; Chen, Z. P.; Nie, Z. K., Possibilistic mean-variance models and efficient frontiers for portfolio selection problem, Inf. Sci., 177, 2787-2801 (2007) · Zbl 1286.91131 |
| [15] | Huang, X., Fuzzy chance-constrained portfolio selection, Appl. Math. Comput., 177, 500-507 (2006) · Zbl 1184.91191 |
| [16] | Heaton, J.; Lucas, D., Portfolio choice in the presence of background risk, Econ. J., 110, 1-26 (2000) |
| [17] | Eeckhoudt, L.; Gollier, C.; Schlesinger, H., Economic and Financial Decisions under Risk (2005), Princeton University Press: Princeton University Press Princeton, NJ |
| [18] | Gollier, C., The Economics of Risk and Time (2001), MIT Press: MIT Press Cambridge · Zbl 0991.91001 |
| [19] | Tsanakas, A., Risk measurement in the presence of background risk, Insurance Math. Econ., 42, 520-528 (2008) · Zbl 1152.91607 |
| [20] | Baptista, A. M., Optimal delegated portfolio management with background risk, J. Banking Finance, 32, 977-985 (2008) |
| [21] | Eichner, T.; Wagener, A., Tempering effects of (dependent) background risk: a mean-variance analysis of portfolio selection, J. Math. Econ., 48, 422-430 (2012) · Zbl 1263.91022 |
| [24] | Cardak, B. A.; Wilkins, R., The determinants of household risky asset holdings: Australian evidence on background risk and other factors, J. Banking Finance, 33, 850-860 (2009) |
| [25] | Jiang, C. H.; Ma, Y. K.; An, Y. B., An analysis of portfolio selection with background risk, J. Banking Finance, 34, 3055-3060 (2010) |
| [26] | Alghalith, M., The impact of background risk, Phys. A Stat. Mech. Appl., 391, 6506-6508 (2012) |
| [27] | Menoncin, F., Optimal portfolio and background risk: an exact and approximated solution, Insurance Math. Econ., 31, 249-265 (2002) · Zbl 1055.91054 |
| [28] | Carlsson, C.; Fullér, R., On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets Syst., 122, 315-326 (2001) · Zbl 1016.94047 |
| [29] | Zhang, W. G.; Nie, Z. K., On possibilistic variance of fuzzy numbers, Lect. Notes Artif. Intell., 2639, 398-402 (2003) · Zbl 1026.68672 |
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