The Fully Nonlinear Stochastic Impulse Control Problem

TL;DR

This paper develops sharp estimates for solutions to a class of free boundary problems related to stochastic impulse control, extending existing methods to more general obstacle conditions.

Contribution

It introduces a novel approach to estimate solutions of obstacle-type free boundary problems with general semi-convex obstacles, applicable to nonlinear stochastic impulse control.

Findings

Established sharp estimates independent of obstacle semi-convexity

Extended free boundary problem analysis to fully nonlinear stochastic control

Provided new bounds for solutions in stochastic impulse control scenarios

Abstract

In this paper, motivated by a problem in stochastic impulse control theory, we aim to study solutions to a free boundary problem of obstacle-type. We obtain sharp estimates for the solution using nonlinear tools which are independent of the modulus of semi-convexity of the obstacle. This allows us to state a general estimate for solutions to free boundary problems of obstacle-type admitting obstacles with a general modulus of semi-convexity. As an application we prove sharp estimates for the solution to a fully nonlinear stochastic impulse control problem.