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

• Main Authors: Dan Zhu, Chuancun Yin
• Format: Article
• Language: English
• Published: Hindawi Limited 2018-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2018/7928953

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.