Fuzzy Malliavin derivative and linear Skorohod fuzzy stochastic differential equation

Article type: Research Article

Authors: Jafari, Hossein^a | Farahani, Hamed^a | Paripour, Mahmoud^{b; *}

Affiliations: [a] Department of Mathematics, Chabahar Maritime University, Iran | [b] Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan, Iran

Correspondence: [*] Corresponding author. Mahmoud Paripour, Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan 65155-579, Iran. E-mail: [email protected].

Abstract: We extend the definitions of the Gaussian Malliavin calculus operators to fuzzy stochastic processes. We consider Skorohod fuzzy stochastic differential equations, which the integrands of the stochastic integrals are not adapted to the filtration generated by a Wiener process. Such equations with randomness, fuzziness and non-adapted processes can be applied in financial models. We apply the fuzzy Malliavin derivative and related topics to discuss the existence and uniqueness of solutions.

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

DOI: 10.3233/JIFS-18043

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2447-2458, 2018