SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS

doi:10.1016/S0252-9602(18)30774-4

Abstract

Abstract:

The local existence and uniqueness of the solutions to backward stochastic differential equations(BSDEs, in short) driven by both fractional Brownian motions with Hurst parameter H∈(1/2,1) and the underlying standard Brownian motions are studied. The generalization of the Itô formula involving the fractional and standard Brownian motions is provided. By theory of Malliavin calculus and contraction mapping principle, the local existence and uniqueness of the solutions to BSDEs driven by both fractional Brownian motions and the underlying standard Brownian motions are obtained.

Key words: Backward stochastic differential equations, malliavin calculus, fractional Brownian motions, Itô, formula

Yuecai HAN, Yifang SUN. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J].Acta mathematica scientia,Series B, 2018, 38(2): 681-694.

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