带注资的经典风险模型中征税问题  

TAXATION PROBLEMS IN THE CLASSICAL RISK MODEL WITH CAPITAL INJECTIONS

作　　者：刘晓[1,2] 陈振龙[2] 

机构地区：[1]安徽师范大学数学计算机科学学院,芜湖241003 [2]浙江工商大学统计与数学学院,杭州310018

出　　处：《系统科学与数学》2015年第2期206-213,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11371321);安徽省哲学社会科学规划项目(AHSK11-12D128);安徽省教育厅自然科学研究重点项目(KJ2012ZD01)资助课题

摘　　要：在带注资的经典风险模型中研究征税问题.假设税收按照loss-carry-forward制度支付.当盈余低于0时,将采取注资的方式使得盈余达到0而不致破产.利用微分法,得到了期望折现征税总额减去期望折现注资成本总额(V(x))满足的积分-微分方程,给出了初始盈余趋于无穷时V(x)的极限值,并在指数理赔假设下给出了V(x)的显式表达式.除此之外,还给出了一个例子.In this paper, we study the taxation problems in the classical risk model with capital injections. Assume that the taxes are paid according to a loss-carry- forward system. Once the surplus is below O, we let the surplus attain 0 avoiding ruin by capital injections. Applying the ＂differential argument＂, the integro-differential equation for the total expected discounted tax payments minus the total expected discounted costs of capital injections （V（x）） is derived, the limitation of V（x） is given when the initial surplus x tends to infinity, and the explicit expression for V（x） is obtained under the assumption that the claim sizes are exponentially distributed. In addition, an example is presented.

关 键 词：征税 注资 LAPLACE变换 

分 类 号：F810.42[经济管理—财政学] F840.31[理学—概率论与数理统计] F840.4[理学—数学] O211.6