Related papers: A forward scheme with machine learning for forward…

We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of \textit{forward optimized certainty equivalent (forward…

A new gradient-based optimization approach by automatically scheduling the learning rate has been proposed recently, which is called Binary Forward Exploration (BFE). The Adaptive version of BFE has also been discussed thereafter. In this…

Deep unfolding neural networks derived from iterative optimization schemes and numerical ordinary/partial differential equations (ODEs/PDEs) have attracted much attention in data science over the last decade. Therein, numerous important…

This work introduces hybrid stochastic differential equations with memory (mH-SDEs), a new class of stochastic systems where transition rates depend on the joint history of both Euclidean and discrete components. This extends existing…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…

Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…

In this paper, we prove the existence and uniqueness of the solution of a coupled Mean-Field Forward-Backward SDE system with Jumps. Then, we give an application in the field of storage problem in smart grids, studied in [4] in the case…

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…

We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward (FBF) algorithm, which is known in the deterministic…

Backpropagation algorithm has been widely used as a mainstream learning procedure for neural networks in the past decade, and has played a significant role in the development of deep learning. However, there exist some limitations…

We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves…

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…

The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic…

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…

Although having been developed for more than two decades, the theory of forward backward stochastic differential equations is still far from complete. In this paper, we take one step back and investigate the formulation of FBSDEs. Motivated…

Federated learning (FL), which has gained increasing attention recently, enables distributed devices to train a common machine learning (ML) model for intelligent inference cooperatively without data sharing. However, problems in practical…

In this paper, we consider the fully coupled forward-backward stochastic functional differential equations (FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward…

Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…