Forward-backward SDEs with discontinuous coefficients

作者：Chen Jianfu; Ma Jin^*; Yin Hong

来源：Stochastic Analysis and Applications, 2018, 36(2): 274-294.

DOI：10.1080/07362994.2017.1399799

• Forward-backward SDEs
• decoupling function
• discontinuous coefficients
• distribution solution
• weak solution
• Krylov estimates
• strong solution

In this paper, we are interested in the well-posedness of a class of fully coupled forward-backward SDE (FBSDE) in which the forward drift coefficient is allowed to be discontinuous with respect to the backward component of the solution. Such an FBSDE is motivated by a practical issue in regime-switching term structure interest rate models, and the discontinuity makes it beyond any existing framework of FBSDEs. In a Markovian setting with non-degenerate forward diffusion, we show that a decoupling function can still be constructed and that it is a Sobolev solution to the corresponding quasilinear PDE. As a consequence we can then argue that the FBSDE admits a weak solution in the sense of [1, 2]. In the one-dimensional case, we further prove that the weak solution of the FBSDE is actually strong, and it is pathwisely unique. Our approach does not use the well-known Yamada-Watanabe Theorem, but instead follows the idea of Krylov for SDEs with measurable coefficients.

• 出版日期2018