Stochastic maximum principle for weighted mean-field system

TL;DR

This paper develops a stochastic maximum principle for weighted mean-field systems where coefficients depend on the state, its weighted measure, and control, with applications to insurance asset-liability management.

Contribution

It introduces a novel maximum principle for weighted mean-field systems with state and measure-dependent coefficients, expanding control theory in this area.

Findings

Established a stochastic maximum principle for the new class of systems.

Applied the theory to optimize insurance premium policies.

Demonstrated effectiveness through a practical asset-liability management example.

Abstract

We study the optimal control problem for a weighted mean-field system. A new feature of the control problem is that the coefficients depend on the state process as well as its weighted measure and the control variable. By applying variational technique, we establish a stochastic maximum principle. As an application, we investigate the optimal premium policy of an insurance firm for asset-liability management problem.