【作者】 苏桂春；

【导师】 牛明飞；

【作者基本信息】 兰州大学 ， 应用数学， 2010， 硕士

【摘要】 破产,是指保险人在拥有一定初始资产的前提下,经过一段时间的经营,盈余第一次变为负值的情况,只是一个数学概念,并不一定意味着保险公司就此倒闭。在现代破产理论中,普遍关注的三个重要指标是：破产概率、破产时间、破产前瞬时盈余和破产赤字之间的关系。Hans U.Gerber和Elias S.W.Shiu构造了著名的期望折现罚金函数,也叫做Gerber-Shiu罚金折现函数。该函数引入破产前瞬时盈余和破产赤字两个指标,非常方便的刻画了破产概率、破产事件的Laplace变换以及破产前瞬时盈余与破产赤字的联合密度函数间关系。保险风险模型中的分红策略最初由De Finetti提出,旨在更实际的反应一个保险投资组合的现金流。之后,与盈余有关的两种分红策略引起了我们的重视：一种是常数值红利边界风险模型又称为完全分红模型,当盈余低于一个常值时,没有红利发给股东或者投保人,然而,盈余一旦高于此边界,则超过的全部盈余都作为红利发给股东,Gerber最初研究了这种策略。另一种是阈红利边界策略,这种风险模型规定,当盈余高于边界时,则红利以低于保费收入的部分发给股东或者投保人,这个策略首先是Gerber、Buhlmann提出,之后在常数边界和依赖于时间的线性边界下,许多学者作了许多工作。本文引入上述两种分红策略以及经典风险模型为基础,同时引入相依风险和带扰动的经典风险模型,然后得出上述对两种分红策略有关结论进行推广,首先引入常数红利边界下阈红利策略,并给出该模型下Gerber-Shiu罚金折现函数,同时给出了线性边界下Gerber-Shiu罚金折现函数结果；引入线性边界下阈红利策略和相依风险模型同时给出满足这两种情况的Gerber-Shiu罚金折现函数；引入带扰动风险模型,得出这种情况下的生存概率、红利付款的期望现值、Gerber-Shiu罚金折现函数等结果。更多还原

【Abstract】 Ruin theory means that insurers have some initial premise of the assets, after a period of operation, Surplus for the first time into a negative situation, only a mathematical concept, this failure does not necessarily mean the insurance company ruin. In modern Ruin theory, three important indicators of general concern are:the time of Ruin, the deficit at ruin, the surplus immediately before the time of ruin.Hans U. Gerber and EliasS.W.Shiu constructed the famous expected dis-counted penalty function, also called Gerber-Shiu discounted penalty function. The instantaneous profit function is the deficit at ruin and the surplus immediately prior to ruin two indicators, Very convenient to describe the probability of Ruin, ruin events prior to the insolvency of the Laplace transform as well as the deficit at ruin and the surplus immediately prior to ruin between the joint density function.Insurance risk model in the initial dividend strategy proposed by the De Finetti, more realistic response to an insurance portfolio cash flow. After two kinds of dividend strategy attracted our attention:one is the constant value Dividend risk model is also known as total dividend model, when the surplus under a constant value, no dividends to shareholders or the insurant, However, once surplus above this boundary, all the surplus over all as a dividend to shareholders, Gerber initial study of this strategy. The other is the threshold dividend strategy, the provisions of this risk model, when the surplus above the boundary, then the dividend less than the premium income to shareholders or policyholders part of this strategy first Gerber, Buhlmann presented, followed by the boundary and depends on the time constant of the linear boundary, many scholars made a lot of work. This dividend strategy and the introduction of the two classical risk model, while the introduction of dependent risks and the classical risk model with a disturbance, and then draw the relevant conclusions of the two dividend strategy to promote, first introduced under the threshold constant Dividend dividend strategy, given the model Gerber-Shiu discounted penalty function, the linear Dividend Barrier is given under the Gerber-Shiu discounted penalty function results; the introduction of linear Dividend Barrier and dependent under the threshold dividend strategy risk model is given to satisfy these two situation Gerber-Shiu discounted penalty function; the introduction of the risk model perturbed obtained the probability of survival under such circumstances, the present value of expected dividend payments, Gerber-Shiu discounted penalty function and other results.更多还原