Numerical Schemes for Multivalued Backward Stochastic Differential Systems

TL;DR

This paper introduces numerical approximation schemes for complex multivalued backward stochastic differential systems within a Markovian setting, combining Euler and Yosida techniques for improved computational methods.

Contribution

It presents a novel mixed approximation scheme for decoupled forward reflected SDEs and backward stochastic variational inequalities, enhancing numerical solutions for these systems.

Findings

Developed an Euler-based approximation scheme.

Integrated Yosida approximation techniques.

Applicable to generalized backward stochastic systems.

Abstract

We define some approximation schemes for different kinds of generalized backward stochastic differential systems, considered in the Markovian framework. We propose a mixed approximation scheme for a decoupled system of forward reflected SDE and backward stochastic variational inequality. We use an Euler scheme type, combined with Yosida approximation techniques.