Optimization of dividend and reinsurance strategies under ruin probability constraint

TL;DR

This paper develops a stochastic control model for insurance companies to optimize dividend and reinsurance strategies while respecting ruin probability constraints, balancing risk and return.

Contribution

It introduces a novel approach to solving nonlinear regular-singular stochastic control problems with ruin probability constraints in insurance.

Findings

Derived optimal retention ratio and dividend payout level.

Established a risk-based capital standard.

Analyzed the impact of risk level on control strategies.

Abstract

This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. However, if the optimal dividend barrier is too low to be acceptable, it will make the company result in bankruptcy soon. Moreover, although risk and return should be highly correlated, over-risking is not a good recipe for high return, the supervisors of the company have to impose their preferred risk level and additional charge on firm seeking services beyond or lower than the preferred risk level. These indeed are nonlinear regular-singular stochastic optimal problems under ruin probability constraints. This paper aims at solving this kind of the optimal problems, that is, deriving the optimal retention ratio,dividend payout level, optimal return function and optimal control strategy of the insurance company. As a by-product, the paper also sets a risk-based capital standard to ensure the capital requirement of can cover the total given risk, and the effect of the risk level on optimal retention ratio, dividend payout level and optimal control strategy are also presented.