Value Function Computation in Fuzzy Models by Differential Evolution

In this paper, we show that the possibilistic mean values produce computation results that may differ in a nontrivial may from those obtained with the fuzzy extension principle. The evidence is carried out by comparing some examples derived from several models in finance.

[1]  Luciano Stefanini,et al.  Parametrized Fuzzy Numbers for Option Pricing , 2007, 2007 IEEE International Fuzzy Systems Conference.

[2]  Fitting prices with a complete model , 2006 .

[3]  Zdenek Zmeskal,et al.  Application of the Fuzzy - Stochastic Methodology to Appraising the Firm Value as a European Call Option , 2001, Eur. J. Oper. Res..

[4]  A. Thavaneswaran,et al.  Option valuation model with adaptive fuzzy numbers , 2007, Comput. Math. Appl..

[6]  Jungang Li,et al.  Strong Solution of Set-Valued Stochastic Differential Equation , 2008, SMPS.

[7]  Luciano Stefanini,et al.  Fuzzy uncertainty in the heston stochastic volatility model , 2011 .

[8]  Luciano Stefanini,et al.  A Parameterization of Fuzzy Numbers for Fuzzy Calculus and Application to the Fuzzy Black-Scholes Option Pricing , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[9]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[10]  Maria Letizia Guerra,et al.  Fuzzy Option Value with Stochastic Volatility Models , 2009, 2009 Ninth International Conference on Intelligent Systems Design and Applications.

[11]  Christer Carlsson,et al.  A Fuzzy Approach to Real Option Valuation , 2002, Fuzzy Sets Syst..

[12]  Hsien-Chung Wu,et al.  Using fuzzy sets theory and Black-Scholes formula to generate pricing boundaries of European options , 2007, Appl. Math. Comput..

[13]  Luciano Stefanini,et al.  Parametric representation of fuzzy numbers and application to fuzzy calculus , 2006, Fuzzy Sets Syst..

[14]  Luciano Stefanini,et al.  Option price sensitivities through fuzzy numbers , 2011, Comput. Math. Appl..

[15]  Luciano Stefanini Differential Evolution Methods for LU-fuzzy Arithmetic , 2007, EUSFLAT Conf..

[16]  Christer Carlsson,et al.  On Possibilistic Mean Value and Variance of Fuzzy Numbers , 1999, Fuzzy Sets Syst..

[17]  Masami Yasuda,et al.  A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty , 2006, Fuzzy Sets Syst..

[18]  Aihong Ren,et al.  Representation theorems, set-valued and fuzzy set-valued Ito integral , 2007, Fuzzy Sets Syst..

[19]  Hsien-Chung Wu,et al.  Pricing European options based on the fuzzy pattern of Black-Scholes formula , 2004, Comput. Oper. Res..

[20]  Yue Zhang,et al.  Fuzzy pricing of geometric Asian options and its algorithm , 2015, Appl. Soft Comput..

[21]  Yuji Yoshida,et al.  The valuation of European options in uncertain environment , 2003, Eur. J. Oper. Res..

[22]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..