Non-Markovian Forward-Backward Stochastic Differential Equations with Discontinuous Coefficients

• 作者: Yin Hong
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: NON-MARKOVIAN FORWARD-BACKWARD SDEs DISCONTINUOUS COEFFICIENTS Krylov ESTIMATES WEAK Solution
• 年，卷（期）: yysxyw_2020,（4）
• 页码范围: 328-343
• 页数: 16页
• 分类号: O17

摘要

In this paper, the existence and uniqueness of a weak solution in the sense of [1] and [2] has been shown for a class of fully coupled forward-backward SDE (FBSDE) such that the forward drift coefficient is allowed to be discontinuous with respect to the backward component of the solution. The novelty of this paper lies on the fact that the FBSDE is non-Markovian, i.e., the coefficients of the FBSDEs are allowed to be random. This type of FBSDEs is inspired by the regime shift model, where the short term interest rate switches between regimes according to the rate level. As a consequence, the discontinuity of the system becomes inevitable, making it violate the usual assumptions of most existing results for FBSDEs. We show the weak well-posedness of the FBSDE by an approximation scheme, along with the decoupling strategy.