Portfolios optimization with coherent risk measures in fuzzy asset management

An portfolio optimization problem with fuzzy random variables is discussed. Risk measures for fuzzy random variables are introduced by perception-based approach. Randomness is estimated stochastically, and fuzziness are evaluated by the mean values with evaluation weights and λ-mean functions. Using coherent risk measures, we discuss a portfolio optimization problem under randomness and fuzziness. By analytical approach, we derive a solution of the portfolio problem. A numerical example is given to explain the results.

[1]  Tanja Neumann.  Mean Variance Analysis In Portfolio Choice And Capital Markets , 2016 .

[2]  S. Pliska.  Introduction to Mathematical Finance: Discrete Time Models , 1997 .

[3]  M. Kratz,et al.  What is the Best Risk Measure in Practice? A Comparison of Standard Measures , 2013, 1312.1645.

[4]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[5]  A. Whitehead.  An Introduction to Mathematics , 1949, Nature.

[6]  Ola Mahmoud,et al.  A Probability Metrics Approach to Financial Risk Measures , 2016 .

[7]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[8]  S. Kusuoka.  On law invariant coherent risk measures , 2001 .

[9]  Marc C. Steinbach,et al.  Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis , 2001, SIAM Rev..

[10]  Marc Roubens,et al.  Ranking and defuzzification methods based on area compensation , 1996, Fuzzy Sets Syst..

[11]  Viswanathan Arunachalam,et al.  Introduction to Mathematical Finance , 2012 .

[12]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[13]  W. Sharpe,et al.  Mean-Variance Analysis in Portfolio Choice and Capital Markets , 1987 .

[14]  Yuji Yoshida.  Perception-Based Estimations of Fuzzy Random Variables: Linearity and convexity , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[15]  Junzo Watada,et al.  Fuzzy-Portfolio-Selection Models With Value-at-Risk , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Amir Ahmadi-Javid,et al.  Entropic Value-at-Risk: A New Coherent Risk Measure , 2012, J. Optim. Theory Appl..

[17]  Y. Yoshida.  "Mean Values, Measurement of Fuzziness and Variance of Fuzzy Random Variables for Fuzzy Optimization" , 2006 .

[18]  Yuji Yoshida.  Fuzzy Extension of Estimations with Randomness: The Perception-Based Approach , 2007, MDAI.

[19]  Yuji Yoshida.  An estimation model of value-at-risk portfolio under uncertainty , 2009, Fuzzy Sets Syst..

[20]  R. Kruse,et al.  Statistics with vague data , 1987 .

[21]  Yuji Yoshida.  A Risk-Minimizing Model Under Uncertainty in Portfolio , 2007, IFSA.

[22]  Stoyan V. Stoyanov,et al.  A Probability Metrics Approach to Financial Risk Measures: Rachev/A Probability Metrics Approach to Financial Risk Measures , 2011 .