Classical Solutions of Path-dependent PDEs and Functional Forward-Backward Stochastic Systems

In this paper we study the relationship between functional forward-backward stochastic systems and path-dependent PDEs. In the framework of functional It\^o calculus, we introduce a path-dependent PDE and prove that its solution is uniquely determined by a functional forward-backward stochastic system.Comment: arXiv admin note: text overlap with arXiv:1108.431

Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs

This paper explores the relationship between non-Markovian fully coupled forward-backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional It\^{o} calculus. Under mild hypotheses, we prove that the forward-backward stochastic system provides the unique classical solution to the path-dependent PDE.Comment: arXiv admin note: text overlap with arXiv:1108.431

Solutions for Functional Fully Coupled Forward-Backward Stochastic Differential Equations

In this paper, we study a functional fully coupled forward-backward stochastic differential equations (FBSDEs). Under a new type of integral Lipschitz and monotonicity conditions, the existence and uniqueness of solutions for functional fully coupled FBSDEs is proved. We also investigate the relationship between the solution of functional fully coupled FBSDE and the classical solution of the path-dependent partial differential equation (P-PDE). When the solution of the P-PDE has some smooth and regular properties, we solve the related functional fully coupled FBSDE and prove the P-PDE has a unique solution

A New Distribution-Random Limit Normal Distribution

This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model