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该文将随机保费收入、相依索赔以及随机分红策略引入到复合二项风险模型中,并研究该模型下的随机分红问题.运用母函数的方法,推导得到保险公司直至破产前的期望累积折现分红量满足的差分方程及其解.最后,通过几个数值例子展示了所得结果. 相似文献
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考虑常数分红界下带扰动的马尔可夫调制对偶风险模型,其中保险公司收益到达过程、收益额的大小以及支出都受一马尔可夫过程的影响,得到了破产前累积分红折现均值所满足的积分一微分方程及边界条件;进一步得到了两状态下,收益分布为指数分布和混合指数分布时累积分红折现均值的表达式,最后给出了数值模拟实例. 相似文献
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考虑一类带随机收入的离散时间风险模型.通过常数分红边界的引入,考虑分红总量的期望折现以及该分红总量的期望效用. 相似文献
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研究了一类相依索赔的离散风险模型,得到了利率为0时模型的最终破产概率所满足的积分方程,以及破产持续n期的概率所满足的表达式.进而,得到了利率不为0时该模型的最终破产概率所满足的积分方程,并利用鞅论技巧导出了最终破产概率的一个Lundberg型上界,最后运用Matlab软件随机模拟破产概率并与Lundberg型上界作比较. 相似文献
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将保险公司各期净损失相互独立的假定改进为依随机序正相依.在相依风险下,利用动态规划原理和状态空间约简,刻画了最优分红策略,证明了区域策略最优,同时讨论了值函数的性质,并给出了数值算法.其中,对涉及独立假定的结论,给出了相依条件下的相应结果,对未涉及独立假定的部分结论也做了改进.研究发现,与独立情形不同,在依随机序正相依风险下,保险公司不必以概率1破产. 相似文献
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该文研究了绝对破产下具有贷款利息及常数分红界的扰动复合Poisson风险模型,得到了折现分红总量的均值函数,及其矩母函数以及此模型的期望折现罚金函数(Gerber-Shiu函数)满足的积分-微分方程及边值条件,并求出了某些特殊情形下的具体表达式. 相似文献
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考虑了具有常红利边界和延迟索赔的一类离散更新风险模型,其中间隔索赔到达时间从离散phase-type分布.定义了两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔会以一定的概率被延迟到下一时段.通过引入辅助风险模型,推导了破产前红利折现期望满足的差分方程及其解.最后给出了当索赔额服从几何分布时的有关数值例子. 相似文献
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In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy (PCT). Integro-differential equations (IDE) for its Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations. 相似文献
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This paper attempts to study the dividend payments in a compound Poisson surplus process with debit interest. Dividends are paid to the shareholders according to a barrier strategy. An alternative assumption is that business can go on after ruin, as long as it is profitable. When the surplus is negative, a debit interest is applied. At first, we obtain the integro‐differential equations satisfied by the moment‐generating function and moments of the discounted dividend payments and we also prove the continuous property of them at zero. Then, applying these results, we get the explicit expressions of the moment‐generating function and moments of the discounted dividend payments for exponential claims. Furthermore, we discuss the optimal dividend barrier when the claim sizes have a common exponential distribution. Finally, we give the numerical examples for exponential claims and Erlang (2) claims. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion 总被引:2,自引:0,他引:2
In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process perturbed by diffusion. Dividends are paid at a constant rate whenever the modified surplus is above the threshold, otherwise no dividends are paid. Two integro-differential equations for the expected discounted dividend payments prior to ruin are derived and closed-form solutions are given. Accordingly, the Gerber–Shiu expected discounted penalty function and some ruin related functionals, the probability of ultimate ruin, the time of ruin and the surplus before ruin and the deficit at ruin, are considered and their analytic expressions are given by general solution formulas. Finally the moment-generating function of the total discounted dividends until ruin is discussed. 相似文献
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David Landriault 《Insurance: Mathematics and Economics》2008,42(1):31-38
The risk model with interclaim-dependent claim sizes proposed by Boudreault et al. [Boudreault, M., Cossette, H., Landriault, D., Marceau, E., 2006. On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actur. J., 265-285] is studied in the presence of a constant dividend barrier. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Finally, we analyze the expected present value of dividend payments before ruin in the same class of risk models. An homogeneous integro-differential equation is derived and then solved. Its solution can be expressed as a different combination of the two fundamental solutions to the homogeneous integro-differential equation associated to the Gerber-Shiu discounted penalty function. 相似文献
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In this paper, we consider a diffusion perturbed classical compound Poisson risk model in the presence of a linear dividend barrier. Partial integro-differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived. Moreover, explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential. We also provided some numerical examples to illustrate the applications of the explicit solutions. Finally we derive partial integro-differential equations with boundary conditions for the Gerber-Shiu function. 相似文献
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In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer's arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends. 相似文献
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In this paper,we consider a risk model in which each main claim may induce a delayed claim,called a by-claim.We assume that the time for the occurrence of a by-claim is random.We investigate the expected discounted penalty function,and derive the defective renewal equation satisfied by it.We obtain some explicit results when the main claim and the by-claim are both exponentially distributed,respectively.We also present some numerical illustrations. 相似文献
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This paper considers a perturbed renewal risk process in which the inter-claim times have a phase-type distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the mth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example. 相似文献
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考虑带利率和常数红利边界的对偶风险模型.首先,给出破产为止总红利现值的期望满足的积分-微分方程,并且在指数收益下得到其封闭解.其次,推导出总红利现值的矩满足的积分-微分方程,在指数收益下给出其封闭解.最后,给出在特殊情形下的数值计算. 相似文献