An anticipating class of Fuzzy Stochastic Differential Equations

Subject Areas : Numerical Methods in Mathematical Finance

Hossein Jafari ¹ , Hamed Farahani ² , Mahmoud Paripour ³

1 - Department of Mathematics, Chabahar Maritime University, Iran
2 - Department of Mathematics, Chabahar Maritime University, Iran.
3 - Hamedan University Of Technology, Hamedan, 65169-13418, Iran.

Received: 2021-01-25 Accepted : 2022-04-24 Published : 2023-05-01

Keywords: Fuzzy stochastic integral, Skorohod integral, Malliavin calculus, Fuzzy stochastic process,

Abstract :

We consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied in financial models. We discuss the existence and uniqueness of strong solutions.We consider a class of fuzzy stochastic differential equations (FSDE), in which the integrands of thestochastic integrals are not adapted to the duration generated by a Wiener process. Such equations with randomness, fuzziness, and non-adapted processes can be applied in financial models. We discuss the existence and uniqueness of strong solutions.

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