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

作     者：Yi-dong WU Jun-yi GUO 

作者机构：School of Mathematical Sciences and LPMCNankai UniversityTianjin 300071China School of EconomicsYunnan UniversityKunming 650091China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2012年第28卷第3期

页      面：505-524页

核心收录：

学科分类：12[管理学] 02[经济学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 071101[理学-系统理论] 0711[理学-系统科学] 0202[经济学-应用经济学] 1204[管理学-公共管理] 020204[经济学-金融学（含∶保险学）] 081101[工学-控制理论与控制工程] 120404[管理学-社会保障] 0811[工学-控制科学与工程] 0701[理学-数学] 

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) 

主　　题：proportional reinsurance non-cheap optimal dividend capital injections 

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.