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This paper considers nonlinear regular-singular stochastic optimal control oflarge insurance company. The company controls the reinsurance rate and dividendpayout process to maximize the expected present value of the dividend pay-outsuntil the time of bankruptcy. However, if the optimal dividend barrier is toolow to be acceptable, it will make the company result in bankruptcy soon.Moreover, although risk and return should be highly correlated, over-risking isnot a good recipe for high return, the supervisors of the company have toimpose their preferred risk level and additional charge on firm seekingservices beyond or lower than the preferred risk level. These indeed arenonlinear regular-singular stochastic optimal problems under ruin probabilityconstraints. This paper aims at solving this kind of the optimal problems, thatis, deriving the optimal retention ratio,dividend payout level, optimal returnfunction and optimal control strategy of the insurance company. As aby-product, the paper also sets a risk-based capital standard to ensure thecapital requirement of can cover the total given risk, and the effect of therisk level on optimal retention ratio, dividend payout level and optimalcontrol strategy are also presented.

Optimization of dividend and reinsurance strategies under ruin probability constraint