A Perception-Based Portfolio Under Uncertainty: Minimization of Average Rates of Falling
- 623 Downloads
A perception-based portfolio model under uncertainty is discussed. In the proposed model, randomness and fuzziness are evaluated respectively by the probabilistic expectation and the mean values with evaluation weights and λ-mean functions. The means, the variances and the covariances fuzzy numbers/fuzzy random variables are evaluated in the possibility case and the necessity case, and the rate of return with portfolios is estimated by the both random factors and imprecise factors. In the portfolio model, the average rate of falling is minimized using average value-at-risks as a coherent risk measure. By analytical approach, we derive a solution of the portfolio problem to minimize the average rate of falling. A numerical example is given to illustrate our idea.
KeywordsFuzzy Number Portfolio Selection Risk Probability Evaluation Weight Short Selling
Unable to display preview. Download preview PDF.
- 6.Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk, 3rd edn. McGraw-Hill, New York (2007)Google Scholar
- 9.Markowitz, H.: Mean-Variance Analysis in Portfolio Choice and Capital Markets. Blackwell, Oxford (1990)Google Scholar
- 10.Pliska, S.R.: Introduction to Mathematical Finance: Discrete-Time Models. Blackwell Publ., New York (1997)Google Scholar
- 12.Rockafellar, R.T., Uryasev, S.P.: Optimization of conditional value-at-risk. Journal of Risk 2, 21–42 (2000)Google Scholar
- 15.Yoshida, Y.: Mean values, measurement of fuzziness and variance of fuzzy random variables for fuzzy optimization. In: Proceedings of SCIS & ISIS 2006, September 2006, pp. 2277–2282 (2006)Google Scholar
- 18.Yoshida, Y.: An estimation model of value-at-risk portfolio under uncertainty. Fuzzy Sets and Systems (to appear) doi:10.1016/j.fss2009.02.007Google Scholar