相关论文: A deep solver for BSDEs with jumps

Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…

We propose a novel computational procedure for quadratic hedging in high-dimensional incomplete markets, covering mean-variance hedging and local risk minimization. Starting from the observation that both quadratic approaches can be treated…

In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153…

We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo…

The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives…

This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T.…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…

We study the properties of nonlinear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale measure associated with a default jump with intensity process $(\lambda_t)$. We give a priori estimates for…

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into…

Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…

In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from…

We study multivalued stochastic differential equations (MSDEs) with maximal monotone operators driven by semimartingales with jumps. We discuss in detail some methods of approximation of solutions of MSDEs based on discretization of…

In this paper, we present a backward deep BSDE method applied to Forward Backward Stochastic Differential Equations (FBSDE) with given terminal condition at maturity that time-steps the BSDE backwards. We present an application of this…

Over the past few years quadratic Backward Stochastic Differential Equations (BSDEs) have been a popular field of research. However there are only very few examples where explicit solutions for these equations are known. In this paper we…

We obtain an existence and uniqueness theorem for fully coupled forward-backward SDEs (FBSDEs) with jumps via the classical solution to the associated quasilinear parabolic partial integro-differential equation (PIDE), and provide the…

As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential…

In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

In this paper, we obtain stability results for backward stochastic differential equations with jumps (BSDEs) in a very general framework. More specifically, we consider a convergent sequence of standard data, each associated to their own…