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

摘要

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