# Time-changed Stochastic Control Problem and its Maximum Principle Theory

## TL;DR

This paper develops a maximum principle framework for stochastic control problems involving time-changed processes driven by Lévy noise, including existence and uniqueness results for associated backward stochastic differential equations.

## Contribution

It introduces a maximum principle theory for time-changed stochastic control problems with Lévy noise and proves existence and uniqueness of related backward stochastic differential equations.

## Key findings

- Established maximum principle for time-changed stochastic control
- Proved existence and uniqueness of time-changed backward SDEs
- Provided illustrative examples

## Abstract

This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a L\'evy noise time-changed by an inverse subordinator. We establish a maximum principle theory for the time-changed stochastic control problem. We also prove the existence and uniqueness of the corresponding time-changed backward stochastic differential equation involved in the stochastic control problem. Some examples are provided for illustration.