Finite Horizon Impulse control of Stochastic Functional Differential Equations

TL;DR

This paper addresses finite horizon impulse control problems for non-Markovian stochastic functional differential equations with control-dependent dynamics, establishing conditions for solvability and trajectory flow properties.

Contribution

It introduces a method to solve finite horizon impulse control problems involving non-Markovian stochastic functional differential equations with control-dependent dynamics.

Findings

Established solvability under functional Lipschitz conditions

Demonstrated the trajectory forms a flow

Extended impulse control theory to non-Markovian dynamics

Abstract

In this work we show that one can solve a finite horizon non-Markovian impulse control problem with control dependant dynamics. This dynamic satisfies certain functional Lipschitz conditions and is path dependent in such a way that the resulting trajectory becomes a flow.