# The Maximum Principle for Progressive Optimal Stochastic Control Problems with Random Jumps

## TL;DR

This paper develops a maximum principle for stochastic control systems with jumps, allowing controls in both diffusion and jump terms without requiring convex control domains, using a novel variation method.

## Contribution

It introduces a new variation method to derive the maximum principle for stochastic systems with jumps, accommodating controls in diffusion and jump components without convexity restrictions.

## Key findings

- Derived the maximum principle for systems with jumps
- Allowed controls in both diffusion and jump terms
- No convexity assumption on control domain

## Abstract

In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to be convex.