Related papers: Solving Backward Doubly Stochastic Differential Eq…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…
In this paper, we present a numerical scheme to solve the initial-boundary value problem for backward stochastic partial differential equations of parabolic type. Based on the Galerkin method, we approximate the original equation by a…
Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool to address such problems under time-independence assumptions. We show how to…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping…
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and…
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
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…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The…
In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…
In this paper, our goal is solving backward doubly stochastic differential equation (BDSDE for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…