The Optimal Portfolio Model Based on Multivariate T Distribution with Fuzzy Math

This paper proposed the optimal portfolio model maximizing returns and minimizing the risk expressed as CvaR under the assumption that the portfolio yield subject to multivariate t distribution. With fuzzy mathematics method, we solve the multi-objectives model, and compare the model results to the case under the assumption of normal distribution yield, based on the portfolio VAR through empirical research. It is showed that our returns and risk are higher than M-V model. LIU Liang, TAN Yuling, HUANG Wenfeng, YU Xing (2012). The Optimal Portfolio Model Based on Multivariate T Distribution with Fuzzy Mathematics Method. Studies in Mathematical Sciences, 4(1), 1-5. Available from: URL: /index. php/sms/article/view/j.sms.1923845220120401.398 DOI: /10.3968/j.sms.1923845220120401.398

Markowitz[1]used the mean-variance and quadratic programming method to solve the optimal portfolio problem, which is considered as the cornerstoneof modernfinancial theory. The model supposes the return of investment has normal distribution, and the investor’s utility function is determined by mean and variance, where the variance reflects the investment risk. Undeniably, Markowitz’s portfolio theory pioneered the quantitative measurement offinancial risk and management, which is followed up by many other theories. With thedeepeningoffinancialtheoryandpracticeoffinancialmeasurementandmodelingtechnology development, the inadequacy of the theory gradually emerged. Firstly, it is the suppose of normal distribution return, with further research and practical testing, some researchers found that assets were heavy-tailed and skewed distribution ,so literatures have improved the suppose. Bollerslev (1987)[2]described the foreign exchange return with t-distributionfirstly. But they did not considered skewed distribution, so income distribution also caused changes in portfolio risk change with the characterization. Hansen (1994)[3]proposed skewed-t-distributionfirstly, and considered both capital gains and fat-tail of the skewed nature of consideration. In recently research, some studies extended the single-variable distribution to multi-variate distribution, such as introducing Copula function. Multi-t distribution also can describe the heavy tail of return.Bao etc supposed hedge portfolio returns subject to multi-t-distribution, whose objective function is to minimize the VAR. They only consider the case of a sub-bit value, not take into account the limits of part

ACKNOWLEDGMENT

This research was partially supported by Hunan University research study and innovative pilot projects.

REFERENCES

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