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Ukrainian Mathematical Journal - We consider a compound Poisson insurance risk model perturbed by diffusion with stochastic return on investment and debit interest. If the initial surplus is... 相似文献
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This study has considered the compound Poisson risk modelperturbed by diffusion with constant interest and obtained an integral-differentialequation for the Gerber-Shiu discounted penalty function. Asymptotic expression forthe ultimate ruin probability also derived across the study. 相似文献
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Zhao Yongxia 《应用概率统计》2013,29(5):495-514
In this paper, we study absolute ruin
problems for the Sparre Andersen risk process with generalized
Erlang()-distributed inter-claim times, investment and debit
interest. We first give a system of integro-differential equations
with certain boundary conditions satisfied by the expected
discounted penalty function at absolute ruin. Second, we obtain a
defective renewal equation under some special cases, then based on
the defective renewal equation we derive two asymptotic results for
the expected discounted penalty function when the initial surplus
tends to infinity for the light-tailed claims and heavy-tailed
claims, respectively. Finally, we investigate some explicit
solutions and numerical results for generalized Erlang(2)
inter-claim times and exponential claims. 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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本文利用齐次泊松过程的可加性,研究了复合泊松过程的可加性及其性质。作为应用,讨论了单个理赔额服从指数分布的复合泊松风险模型在第n次索赔时发生负盈余的概率。 相似文献
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带扩散扰动项的广义双Poisson风险模型下的破产概率 总被引:1,自引:0,他引:1
本文首先在[1]-[4]讨论的基础上,将经典的破产模型推广到带扩散扰动项的广义双Po isson风险模型,即将保费收取过程和索赔总额过程同时推广到广义复合Po isson过程,以此解决在同一时刻有两张以上保单到达和两个以上顾客索赔的实际问题;接着运用鞅方法证明了破产概率满足的Lundberg不等式和一般公式在我们所建的模型下同样成立. 相似文献
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Chun-sheng ZHANG Lian-zeng ZHANG Rong WUDepartment of Mathematics Nankai University Tianjing China 《应用数学学报(英文版)》2002,18(1):153-160
Abstract In the present paper surplus process perturbed by diffusion are considered.The distributions ofthe surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation andruin caused by a claim are studied.Some joint distribution densities are obtained.Techniques from martingaletheory and renewal theory are used. 相似文献
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本文将双复合POISSON风险模型推广到保费随机收取的新模型并考虑了资金利率和通货膨胀率,运用鞅分析方法获得了其破产概率所满足的Lundberg不等式及其一般表达式。 相似文献
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Riccardo Gatto Benjamin Baumgartner 《Methodology and Computing in Applied Probability》2016,18(1):217-235
A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute. 相似文献
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复合广义齐次Poisson过程的多险种破产概率 总被引:11,自引:0,他引:11
于文广 《应用数学与计算数学学报》2003,17(2):63-69
本文推广了经典的复合泊松风险模型,建立了两类复合广义齐次poisson过程的多险种破产模型.对于新模型,我们得到了初始资本为u的破产概率φ(u)的精确表达式以及特殊情况下φ(0)的表达式,并且导出了调节系数方程和调节系数R的上下界. 相似文献
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在经典风险模型基础上,研究了保险公司保费收入和索赔均服从复合泊松过程的双复合泊松风险模型,针对最优投资策略和求解破产时刻惩罚金期望折现函数的问题,利用重期望公式和马氏性得到期望折现函数满足的带边界条件的二阶积分微分方程,通过高效的Sinc数值方法求出折现函数的近似数值解,从而由图像分析破产概率变化的趋势. 相似文献
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我们考虑既带有随机干扰又带有确定投资回报的风险过程, 得到了破产前瞬间盈余的分布$F_{\delta}(u,x)$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}(u,x,y)$所满足的积分表达, 连续性及二次连续可微性和积分--微分方程. 同时, 只有随机干扰的风险模型下的破产前瞬间盈余的分布及破产前瞬间盈余和破产时赤字的联合分布所满足的性质也被得到. 已有文献中的诸多有关结果均可以通过令我们结论中的某些参数特殊化为零而得到. 相似文献
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Yu-Ting Chen 《随机分析与应用》2013,31(5):897-910
Abstract In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where only downward jumps are allowed. 相似文献
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In this paper, we present an approach of changing probability
measures associated with numeraire changes to the pricing of catastrophe event (CAT) derivatives.
We assume that the underlying asset and a discounted zero-coupon bond follow
a stochastic process, respectively. We obtain explicit closed form formulae that permit
the interest rate to be random. We shall see that sometimes it is convenient to change
the numeraire because of modeling considerations as well. Furthermore, we show that,
for compound Poisson losses, sometimes a continuum of jump sizes can be replaced by
finitely many jump sizes. Therefore, sometimes we can explore further applications of
the closed-form formulae beyond the case that the compound Poisson losses are finitely
many jump sizes. Finally, numerical experiments demonstrate how financial risks and
catastrophic risks affect the price of double trigger put option. 相似文献
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分析了带有复合泊松损失过程和随机利率的巨灾看跌期权的定价问题.资产价格通过跳扩散过程刻画,该过程与损失过程相关.当利率过程服从CIR模型时,获得了期权定价的显式解,并给出相关证明.通过一个实例,讨论了资产价格与期权价格的关系. 相似文献
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