## A possibilistic approach to selecting portfolios with highest utility score.(English)Zbl 1027.91038

Summary: The mean-variance methodology for the portfolio selection problem, originally proposed by H. Markowitz [Portfolio selection, J. Finance 7, 77-91 (1952)], has been one of the most important research fields in modern finance. In this paper we assume that: (i) each investor can assign a welfare, or utility, score to competing investment portfolios based on the expected return and risk of the portfolios; and (ii) the rates of return on securities are modelled by possibility distributions rather than probability distributions. We present an algorithm of complexity $$o(n^3)$$ for finding an exact optimal solution (in the sense of utility scores) to the $$n$$-asset portfolio selection problem under possibility distributions.

### MSC:

 91G10 Portfolio theory

### Keywords:

mean-variance analysis; possibility distributions
Full Text:

### References:

 [1] Bodie, Z.; Kane, A.; Marcus, A.J., Investments, times mirror higher education group, (1996), Irwin Boston [2] Carlsson, C.; Fullér, R., On possibilistic Mean value and variance of fuzzy numbers, Fuzzy sets and systems, 122, 315-326, (2001) · Zbl 1016.94047 [3] Inuiguchi, M.; Tanino, T., Portfolio selection under independent possibilistic information, Fuzzy sets and systems, 115, 83-92, (2000) · Zbl 0982.91028 [4] Markowitz, H., Portfolio selection, J. finance, 7, 77-91, (1952) [5] Tversky, A., Intransitivity of preferences, Psychol. rev., 76, 31-45, (1969) [6] Watada, J., Fuzzy portfolio selection and its applications to decision making, Tatra mountains math. publ., 13, 219-248, (1997) · Zbl 0915.90008 [7] Xia, Y.; Liu, B.; Wang, S.; Lai, K.K., A model for portfolio selection with order of expected returns, Comput. oper. res., 27, 409-422, (2000) · Zbl 1063.91519
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.