Related papers: Convergence of a Deep BSDE solver with jumps
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
The aim of this paper is to study an optimal stopping problem for dynamic risk measures induced by backward stochastic differential equations with jumps and delayed generator. Firstly, we connect the value function of this problem to…
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…
Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well…
This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…
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…
We report two methods for solving FBSDEs of path dependent types of high dimensions. Specifically, we propose a deep learning framework for solving such problems using path signatures as underlying features. Our two methods…
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce…
Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually…
Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
Functions with jumps and kinks typically arising from parameter dependent or stochastic hyperbolic PDEs are notoriously difficult to approximate. If the jump location in physical space is parameter dependent or random, standard…
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown…
Reinforcement Learning (RL) has proven effective in solving complex decision-making tasks across various domains, but challenges remain in continuous-time settings, particularly when state dynamics are governed by stochastic differential…
We propose a new method, called a deep-genetic algorithm (deep-GA), to accelerate the performance of the so-called deep-BSDE method, which is a deep learning algorithm to solve high dimensional partial differential equations through their…
The theory of Forward-Backward Stochastic Differential Equations (FBSDEs) paves a way to probabilistic numerical methods for nonlinear parabolic PDEs. The majority of the results on the numerical methods for FBSDEs relies on the global…
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…