Optimal dividend and investing control of a insurance company with higher solvency constraints

TL;DR

This paper develops an optimal control framework for an insurance company's dividends, reinsurance, and investments under solvency constraints, maximizing dividends while ensuring risk-based capital standards.

Contribution

It introduces a comprehensive model combining dividend, reinsurance, and investment controls with solvency constraints, and derives the optimal policies and return functions.

Findings

Optimal control policies for dividends, reinsurance, and investments are characterized.

A risk-based capital standard ensuring solvency is theoretically established.

The model maximizes expected dividends under fixed insolvency probability constraints.

Abstract

This paper considers optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. This paper aims at describing the optimal return function as well as the optimal policy. As a by-product, the paper theoretically sets a risk-based capital standard to ensure the capital requirement of can cover the total risk.