Stochastic Optimal Control of Investment and Dividend Payment Model under Debt Control with Time-Inconsistency

Abstract EN

This paper considers the optimal debt ratio, investment, and dividend payment policies for insurers with time-inconsistency.

The surplus process of an insurance company is determined by the change of asset value and the change of liabilities.

The asset can be invested in financial market which contains a risky asset and a risk-free asset, and when the insurer incurs a liability, he/she earns some premium.

The objective is to maximize the expected nonconstant discounted utility of dividend payment until a determinate time.

This is a time-inconsistent control problem.

We obtain the modified HJB equation and the closed-form expressions for the optimal debt ratio, investment, and dividend payment policies under logarithmic utility.