论文信息 - On Stochastic Differential Equations with Fuzzy Set Coefficients

On Stochastic Differential Equations with Fuzzy Set Coefficients

We define stochastic differential equations with fuzzy set coefficients and prove that their solutions are random fuzzy set processes. This is achieved by obtaining almost sure boundedness of solutions to stochastic differential equations with set coefficients. An example for Black-Scholes market model with expected return ratio being a fuzzy set is also given.

Yukio Ogura | Y. Ogura

[1] Kiyosi Itô. On a stochastic integral equation , 1946 .

[2] R. C. Merton,et al. Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[3] F. Black,et al. The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[4] N. Ikeda,et al. A comparison theorem for solutions of stochastic differential equations and its applications , 1977 .

[5] Y. Ogura,et al. On the strong comparison theorems for solutions of stochastic differential equations , 1981 .

[6] K. Brown,et al. Graduate Texts in Mathematics , 1982 .

[7] L. Rogers. Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[8] B. Øksendal. Stochastic Differential Equations , 1985 .

[9] Ioannis Karatzas,et al. Brownian Motion and Stochastic Calculus , 1987 .

[10] M. Kisielewicz. Properties of solution set of stochastic inclusions , 1993 .

[11] N. Ahmed. Nonlinear stochastic differential inclusions on balance space , 1994 .

[12] V. Kreinovich,et al. Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables , 2002 .

[13] J. Kim,et al. On Set-Valued Stochastic Integrals , 2003 .