Mean reflected stochastic differential equations with two constraints

TL;DR

This paper investigates the existence, uniqueness, and stability of solutions to mean reflected stochastic differential equations with two constraints, where the reflection depends on the law of the solution, with applications in constrained investment models.

Contribution

It introduces a framework for mean reflected SDEs with dual constraints based on the law of the solution, expanding the theory beyond path-dependent reflections.

Findings

Established conditions for existence and uniqueness of solutions.

Proved stability results under perturbations.

Applied the theory to financial investment models with constraints.

Abstract

We study the problem of the existence, uniqueness and stability of solutions of reflected stochastic differential equations (SDEs) with a minimality condition depending on the law of the solution (and not on the paths). We require that some functionals depending on the law of the solution lie between two given c\`adl\`ag constraints. Applications to investment models with constraints are given.