# Stochastic maximum principle for optimal control problem with a stopping time cost functional

## TL;DR

This paper develops a stochastic maximum principle for optimal control problems involving a stopping time cost functional, introducing a discrete terminal system and demonstrating its application through an example.

## Contribution

It presents a novel stochastic maximum principle for control problems with stopping time costs, expanding the theoretical framework in stochastic control.

## Key findings

- Established the stochastic maximum principle for the new control problem
- Introduced a discrete terminal system approach
- Provided an illustrative example of the main results

## Abstract

In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by introducing a discrete terminal system. Finally, we provide an example to describe the main results of this study.