Multi-Criteria Based Robust Markowitz Model under Box Uncertainty

Authors: Pulak Swain, A. K. Ojha

Abstract:

Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of  E- constraint method.

Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.

References:

[1] Markowitz, H., Portfolio Selection, Journal of Finance, Vol. 7, pp. 77-91 (1952).
[2] Markowitz, H., Portfolio Selection: efficient diversification of investments, Basil Blackwell, New York (1959).
[3] Meghwani, S. S., and Thakur, M. Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and evolutionary computation, 37, pp. 104-125 (2017).
[4] Konno, H., Waki, H., and Yuuki, A., Portfolio optimization under lower partial risk measures, Asia-Pacific Financial Markets, Vol. 9(2), pp. 127-140 (2002).
[5] Estrada, J., Mean-semivariance behavior: Downside risk and capital asset pricing. International Review of Economics & Finance, 16(2), pp. 169-185 (2007).
[6] Ben-Tal, A., and Nemirovski, A. Robust solutions of uncertain linear programs. Operations research letters, 25(1), pp. 1-13 (1999).
[7] Ben-Tal and A. Nemirovski. Robust optimization-methodology and applications. Mathematical Programming, 92(3), pp. 453-480 (2002).
[8] Bertsimas, D.B. Brown, and C. Caramanis. Theory and applications of robust optimization problem. SIAM Review. 53(3), pp. 464-501 (2011).
[9] Goldfarb, D., and Iyengar, G., Robust portfolio selection problems. Mathematics of operations research, 28(1), pp. 1-38 (2003).
[10] Rajan, M. P., and Rana, N. , A robust portfolio optimization in Indian Stock market. In 2011 World Congress on Information and Communication Technologies, pp. 645-650 (2011).
[11] Miettinen, K., Nonlinear multiobjective optimization Springer Science & Business Media, Vol. 12, (2012).
[12] Nayak, S., and Ojha, A. K., Multi-objective Linear Fractional Programming Problem with Fuzzy Parameters. In Soft Computing for Problem Solving . Springer, Singapore, pp. 79-90 (2019).
[13] Nayak, S., and Ojha, A., On multi-level multi-objective linear fractional programming problem with interval parameters. RAIRO-Operations Research, 53(5), pp. 1601-1616 (2019).