On interval portfolio selection problem
The future returns of each securities cannot be correctly reflected by the data in the past, therefore the expert’s judgements and experiences should be considered to estimate the security returns for the future. In this paper, we propose an interval portfolio selection model in which both the returns and the risks of assets are defined as intervals. By using interval and convex analysis, we solve this model and get the noninferior solution. Finally, an example is given to illustrate our results. The interval portfolio selection model improves and generalizes the Markowitz’s mean-variance model and the results of Deng et al. (Eur J Oper Res 166(1):278–292, 2005).
KeywordsPortfolio selection Interval Interval analysis Inverse interval matrix
This work was supported by the National Natural Science Foundation of China (71101099, 70831005) and the Special Funds of Sichuan University of the Fundamental Research Funds for the Central Universities (SKQY201330).
- Bertsimas, D., & Thiele, A. (2006). Robust and data-driven optimization: Modern decision making under uncertainty. In Tutorials in operations research (pp. 95–122). INFORMS.Google Scholar
- Elton, E. J., Gruber, M. J., & Urich, T. J. (1978). Are betas best? Journal of Finance, 33(5), 1375–1384.Google Scholar
- Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.Google Scholar
- Markowitz, H. M. (1991). Portfolio selection: Efficient diversification of investments (2nd ed.). Oxford: Basil Blackwell.Google Scholar