This paper considers nonlinear optimal stochastic control of insurance company with proportional reinsurance policy under small bankrupt probability constraints . The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividends 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. In addition , although risk and return should be highly correlated, over-risking is not a good recipe for high return . Therefore, the managements of the company have to impose their preferred risk level and additional charge on firm seeking services beyond or lower than the  level. These turn out to be nonlinear regular-singular stochastic optimal problems under small bankrupt probability constraints. This paper aims at solving this kind of the optimal problems, that is, working out the optimal control policy of the insurance company , in particular, exact minimum dividend barrier, and finding the optimal return function associated with the optimal policy .
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 insolvency 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 policy 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 policy are also presented .
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optimal stochastic control of insurance company with proportional reinsurance policy under small bankrupt probability constraints
regular-singular stochastic optimal control of large insurance company
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dividends
dividend pay-outs
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. Therefore, the managements
, the supervisors
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preferred risk
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turn out to be
indeed are
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small bankrupt
insolvency
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working out the optimal
deriving the optimal retention ratio,dividend payout level, optimal return function and optimal
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, in particular, exact minimum dividend barrier, and finding the optimal return function associated with the optimal policy
. 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 policy are also presented