Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application-Reference-Cited by-同舟云学术

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

Published:2020-11-07 Issue:4 Volume:28 Page:291-306
ISSN:1569-397X
Container-title:Random Operators and Stochastic Equations
language:en
Short-container-title:

Author:

Bouaziz Tayeb¹,Chala Adel¹

Affiliation:

1. Laboratory of Applied Mathematics , University Mohamed Khider , P.O. Box 145 , Biskra 07000 , Algeria

Abstract

Abstract We consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1 )

{H\in(\frac{1}{2},1)}

and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

Publisher

Walter de Gruyter GmbH

Subject

Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rose-2020-2047/pdf

Reference16 articles.

1. F. Biagini, Y. Hu, B. Øksendal and A. Sulem, A stochastic maximum principle for processes driven by fractional Brownian motion, Stochastic Process. Appl. 100 (2002), 233–253.

2. F. Biagini, Y. Hu, B. Øksendal and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Probab. Appl. (N. Y.), Springer, London, 2008.

3. R. Buckdahn and J. Ma, Stochastic viscosity solutions for nonlinear stochastic partial differential equations. I, Stochastic Process. Appl. 93 (2001), no. 2, 181–204.

4. R. Buckdahn and J. Ma, Stochastic viscosity solutions for nonlinear stochastic partial differential equations. II, Stochastic Process. Appl. 93 (2001), no. 2, 205–228.

5. N. El Karoui, S. Peng and M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance. 7 (1997), no. 1, 1–71.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Stochastic controls of fractional Brownian motion;Random Operators and Stochastic Equations;2024-02-01