# Optimal Control of Markov Regime-Switching Stochastic Recursive Utilities

## TL;DR

This paper develops a stochastic maximum principle for optimal control of systems with Markov regime-switching and recursive utilities, addressing non-convex control domains and control-dependent diffusion terms.

## Contribution

It introduces new first and second-order adjoint equations and derives variational equations for forward-backward stochastic differential equations in this context.

## Key findings

- Established a general maximum principle for complex stochastic control systems.
- Derived novel second-order adjoint equations involving solutions of second-order adjoint.
- Provided illustrative examples demonstrating the theoretical results.

## Abstract

In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be convex, and the diffusion terms depend on control variables. To this end, we first study a kind of classical forward stochastic optimal control problems. Afterwards, based on previous results, we introduce two groups of new first and second-order adjoint equations. The corresponding variational equations for forward-backward stochastic differential equations are derived. In particular, the generator in the maximum principle contains solutions of second-order adjoint equation which is novel. Some interesting examples are concluded as well.