A Discrete-Time American Put Option Model with Fuzziness of Stock Prices

  • Authors:

  • Yuji Yoshida;Masami Yasuda;Jun-Ichi Nakagami;Masami Kurano

  • Affiliations:

  • Faculty of Economics and Business Administration, The University of Kitakyushu, Kitakyushu, Japan 802-8577;Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba, Japan 263-8522;Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba, Japan 263-8522;Department of Mathematics, Faculty of Education, Chiba University, Chiba, Japan 263-8522

  • Venue:
  • Fuzzy Optimization and Decision Making
  • Year:
  • 2005

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Abstract

To solve a mathematical model for American put option with uncertainty, we utilize two essentials, i.e., a 驴-weighting function and a mean value of fuzzy random variables simultaneously. Estimation of randomness and fuzziness as uncertainty should be important when we deal with a reasonable and natural model extended from the original optimization/decision making. Three kinds of mean values by fuzzy measures, which are based on Possibility, Necessity and Credibility, are demonstrated particularly. We consider the optimal expected price of the American put option by dynamic programming under a reasonable assumption. A numerical example is given to illustrate our idea.