Theoretical and numerical Analysis on Optimal dividend policy of an insurance company with positive transaction cost and higher solvency

TL;DR

This paper develops a stochastic control model for an insurance company's dividend and reinsurance policies, balancing profit maximization with solvency constraints, and provides explicit solutions and numerical insights on key parameters.

Contribution

It introduces a novel stochastic control framework incorporating positive transaction costs and solvency constraints, deriving explicit optimal policies and value functions.

Findings

Optimal dividend payout and retention ratios depend on volatility and risk level.

The model provides a risk-based capital standard ensuring solvency.

Numerical analysis shows parameter impacts on profit and risk management.

Abstract

Based on a point of view that solvency and security are first, this paper considers regular-singular stochastic optimal control problem of a large insurance company facing positive transaction cost asked by reinsurer under solvency constraint. The company controls proportional reinsurance and dividend pay-out policy to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. The paper aims at deriving the optimal retention ratio, dividend payout level, explicit value function of the insurance company via stochastic analysis and PDE methods. The results present the best equilibrium point between maximization of dividend pay-outs and minimization of risks. The paper also gets a risk-based capital standard to ensure the capital requirement of can cover the total given risk. We present numerical results to make analysis how the model parameters, such as, volatility, premium rate, and risk level, impact on risk-based capital standard, optimal retention ratio, optimal dividend payout level and the company's profit.