Optimal Dividend and Dynamic Reinsurance Strategies with Capital Injections and Proportional Costs  

作　　者：Yi-dong WU Jun-yi GUO 

机构地区：[1]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China [2]School of Economics,Yunnan University,Kunming 650091,China

出　　处：《Acta Mathematicae Applicatae Sinica》2012年第3期505-524,共20页应用数学学报（英文版）

基　　金：Supported by the National Basic Research Program of China (973 Program) (Grant No. 2007CB814905);the National Natural Science Foundation of China (NSFC Grant No. 10871102)

摘　　要：We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of （cheap or non-cheap） proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they axe the same as those in the model of no bankruptcy.We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of （cheap or non-cheap） proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they axe the same as those in the model of no bankruptcy.

关 键 词：proportional reinsurance non-cheap optimal dividend capital injections 

分 类 号：O231[理学—运筹学与控制论] F842.3[理学—数学]