保险风险模型中最优loss-carry-forward赋税问题的研究

发布时间：2018-05-16 04:39

  本文选题：总赋税折现值期望 + 最优loss-carry-forward赋税策略　； 参考：《武汉大学》2013年博士论文

【摘要】：在当今保险精算学的研究领域中,国家税收当局对保险公司的最优loss-carry-forward税征收问题由于具有重要的理论价值和广泛的应用前景,受到众多学者的广泛关注。从某种程度上说,保险公司的赋税问题的研究可以为国家税收当局设计赋税制度提供理论依据。本学位论文将以保险公司的最优赋税问题为主线,结构如下： 第一章,介绍保险精算学家们就loss-carry-forward赋税问题所做的已有工作。 第二章,受到Albrecher和Hipp (2007), Albrecher et al.(2008)以及K yprianou和Zhou (2009)的启发,我们考虑保险公司盈余过程：Rtπ＝Xt-f0tγπ(Sσ)dSσ,其中X是一族谱负的Levy过程(不考虑两种平凡的情形：负的隶属子和线性漂移),表示X的最大值过程,(?)π(St)表示t时刻的loss-carry-forward赋税率(该税率受限于策略π,且为St的函数)。我们的目标是寻找出能让总赋税折现值期望达到最大的赋税策略：Fxf0τπe-ctγπ(St)dSt,其中Ex和τπ分别表示X0=x条件下的条件期望和破产时刻。如果把x对应的尺度函数记为W~c(x),而且γπ(·)取值于[α,β](0≤α≤β1),我们考虑以下两种情况： (a)如果最优的loss-carry-forward赋税策略是从始至终以固定的税率序进行赋税。 (b)如果则最优的loss-carry-forward赋税策略是：当保险公司的盈余水平低于某固定值u0时,以α作为税率进行赋税,而当保险公司的盈余水平高于时u0,用固定税率β进行赋税。 第三章,我们在已考虑(当盈余大于零时进行无风险投资的)常数利息率的Cramer-Lundberg风险模型中研究使到破产时刻为止loss-carry-forward赋税总折现值期望达到最大的最优赋税策略。最优目标函数被证明是一个Hamilton-Jacobi-Bellman万程的经典解,最优赋税策略则被证明是一个band策略。最后,对于指数分布索赔情形,最优目标函数的封闭解也被给出。
[Abstract]:In the field of insurance actuarial research, the issue of optimal loss-carry-forward tax collection by national tax authorities for insurance companies has important theoretical value and wide application prospects, so it has been widely concerned by many scholars. To some extent, the study of the tax issue of insurance companies can provide the theoretical basis for the national tax authorities to design the tax system. This dissertation will focus on the optimal taxation of insurance companies, with the following structure: The first chapter introduces the existing work of the actuaries on loss-carry-forward tax. Chapter II, inspired by Albrecher and Hipp 2007, Albrecher et al. (2008) and K yprianou and Zhou 2009), We consider the insurance company earnings process: RT 蟺 n Xt-f 0t 纬 蟺 -S 蟽 D S 蟽, where X is a genealogically negative Levy process (not taking into account two ordinary cases: negative subordinates and linear drift, representing the maximum value of X) 蟺 S) representing the loss-carry-forward tax rate at t time. The tax rate is limited by the strategy 蟺 and is a function of St. Our goal is to find out a tax strategy: Fxf0 蟿 蟺 e-ct 纬 蟺 Stu dStS, where Ex and 蟿 蟺 represent conditional expectation and ruin time under X0X condition, respectively. If the scale function corresponding to x is denoted as WCX, and the value of 纬 蟺 () is given to [伪, 尾] 0 鈮，

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