Solutions to BSDEs driven by both standard and fractional Brownian motions |
| |
Authors: | Wei-yin Fei Deng-Feng Xia Shu-guang Zhang |
| |
Institution: | 1219. Department of Applied Mathematics, Anhui Polytechnic University, Wuhu, 241000, China 2219. Department of Applied Mathematics, Anhui Polytechnic University, Wuhu, 241000, China 3219. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China
|
| |
Abstract: | The backward stochastic differential equations driven by both standard and fractional Brownian motions (or, in short, SFBSDE) are studied. A Wick-Itô stochastic integral for a fractional Brownian motion is adopted. The fractional Itô formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found. |
| |
Keywords: | fractional Brownian motion Malliavin calculus fractional It6 formula quasi-conditional expec-tation SFBSDE |
本文献已被 维普 SpringerLink 等数据库收录! |
|