首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Optimal dividend policies for piecewise-deterministic compound Poisson risk models
Authors:Runhuan Feng  Hans W Volkmer  Shuaiqi Zhang  Chao Zhu
Institution:1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, USA.rfeng@illinois.edu;3. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, USA.;4. Department of Statistics, Hebei University of Technology, Tianjin, China.
Abstract:This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.
Keywords:piecewise-deterministic compound Poisson model  HJB equation  quasi-variational inequality  threshold strategy  barrier strategy
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号