Solutions to BSDEs driven by both standard and fractional Brownian motions

DOI10.1007/s10255-013-0219-1zbMath1329.60180OpenAlexW1973208575MaRDI QIDQ350757

Dengfeng Xia, Weiyin Fei, Shuguang Zhang

Publication date: 3 July 2013

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-013-0219-1

zbMATH Keywords

fractional Brownian motionMalliavin calculusfractional Itô formulaquasi-conditional expectationSFBSDE

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Financial applications of other theories (91G80) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (12)

Solutions to BSDEs driven by both fractional Brownian motions and the underlying standard Brownian motions ⋮ Solutions to BSDEs driven by multidimensional fractional Brownian motions ⋮ Density estimates for the solutions of backward stochastic differential equations driven by Gaussian processes ⋮ Generalized BDSDEs driven by fractional Brownian motion ⋮ Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients ⋮ Averaging principle for BSDEs driven by two mutually independent fractional Brownian motions ⋮ Maximum principle for mean‐field controlled systems driven by a fractional Brownian motion ⋮ BSDEs driven by two mutually independent fractional Brownian motions with stochastic Lipschitz coefficients ⋮ On existence and uniqueness of solutions to uncertain backward stochastic differential equations ⋮ A general non-existence result for linear BSDEs driven by Gaussian processes ⋮ Anticipated BSDEs driven by two mutually independent fractional Brownian motions with non-Lipschitz coefficients ⋮ Backward SDEs driven by Gaussian processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adapted solution of a backward stochastic differential equation
• Itô's formula with respect to fractional Brownian motion and its application
• Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion
• Stochastic analysis of the fractional Brownian motion
• Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2
• Differential equations driven by fractional Brownian motion
• A stochastic maximum principle for processes driven by fractional Brownian motion.
• Stochastic integration with respect to fractional Brownian motion
• Minimal variance hedging for fractional Brownian motion
• Explicit solutions of a class of linear fractional BSDEs
• Integral transformations and anticipative calculus for fractional Brownian motions
• FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE
• Backward Stochastic Differential Equation Driven by Fractional Brownian Motion
• Stochastic analysis of fractional brownian motions
• Backward Stochastic Differential Equations in Finance
• Arbitrage with Fractional Brownian Motion
• A General Fractional White Noise Theory And Applications To Finance
• OPTIMAL CONSUMPTION AND PORTFOLIO IN A BLACK–SCHOLES MARKET DRIVEN BY FRACTIONAL BROWNIAN MOTION
• Stochastic differential equations for fractional Brownian motions
• Stochastic integration with respect to the fractional Brownian motion
• On the prediction of fractional Brownian motion
• Stochastic Calculus for Fractional Brownian Motion I. Theory
• Stochastic Control for Linear Systems Driven by Fractional Noises
• Fractional Brownian Motions, Fractional Noises and Applications

This page was built for publication: Solutions to BSDEs driven by both standard and fractional Brownian motions