共查询到18条相似文献,搜索用时 109 毫秒
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《数学的实践与认识》2017,(17)
提出了一种保费收取过程为二项过程而索赔过程为其稀疏过程的风险模型,讨论了该模型的Gerber-Shiu折现罚金函数,得到了Gerber-Shiu折现罚金函数所满足的更新方程和渐近估计式,并且根据Gerber-Shiu折现罚金函数的特点,还得到了一些相关精算量的渐近估计式. 相似文献
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本文在经典风险模型下, 引进带有一种随机利率的破产时罚金折现期望的概念, 其利率的随机性通过标准Wiener过程和Poisson过程来描述. 给出破产时罚金折现期望所满足的更新方程, 并利用这个更新方程给出破产时罚金折现期望的渐近公式. 相似文献
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Jianhua ChengDehui Wang 《Applied mathematics and computation》2011,218(7):3822-3833
In this paper, we consider a discrete insurance risk model in which the claims, the premiums and the rates of interest are assumed to have dependent autoregressive structures (AR(1)). We derive recursive and integral equations for expected discounted penalty function. By these equations, we obtain generalized Lundberg inequality for the infinite time severity of ruin and hence for the infinite time ruin probability, consider asymptotic formula for the finite time ruin probability when loss distributions have regularly varying tails, and study some probability properties of the duration of ruin. 相似文献
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In this paper, we consider the Gerber-Shiu expected discounted penalty function for the perturbed compound Poisson risk process with constant force of interest. We decompose the Gerber-Shiu function into two parts: the expected discounted penalty at ruin that is caused by a claim and the expected discounted penalty at ruin due to oscillation. We derive the integral equations and the integro-differential equations for them. By solving the integro-differential equations we get some closed form expressions for the expected discounted penalty functions under certain assumptions. 相似文献
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In this paper, we study absolute ruin questions for the perturbed compound Poisson risk process with investment and debit
interests by the expected discounted penalty function at absolute ruin, which provides a unified means of studying the joint
distribution of the absolute ruin time, the surplus immediately prior to absolute ruin time and the deficit at absolute ruin
time. We first consider the stochastic Dirichlet problem and from which we derive a system of integro-differential equations
and the boundary conditions satisfied by the function. Second, we derive the integral equations and a defective renewal equation
under some special cases, then based on the defective renewal equation we give 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 when claim sizes are exponentially distributed. 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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Consider a compound Poisson surplus process of an insurer with debit interest and tax payments. When the portfolio is in a profitable situation, the insurer may pay a certain proportion of the premium income as tax payments. When the portfolio is below zero, the insurer could borrow money at a debit interest rate to continue his/her business. Meanwhile, the insurer will repay the debts from his/her premium income. The negative surplus may return to a positive level except that the surplus is below a certain critical level. In the latter case, we say that absolute ruin occurs. In this paper, we discuss absolute ruin quantities by defining an expected discounted penalty function at absolute ruin. First, a system of integro-differential equations satisfied by the expected discounted penalty function is derived. Second, closed-form expressions for the expected discounted total sum of tax payments until absolute ruin and the Laplace-Stieltjes transform (LST) of the total duration of negative surplus are obtained. Third, for exponential individual claims, closed-form expressions for the absolute ruin probability, the LST of the time to absolute ruin, the distribution function of the deficit at absolute ruin and the expected accumulated discounted tax are given. Fourth, for general individual claim distributions, when the initial surplus goes to infinity, we show that the ratio of the absolute ruin probability with tax to that without tax goes to a positive constant which is greater than one. Finally, we investigate the asymptotic behavior of the absolute ruin probability of a modified risk model where the interest rate on a positive surplus is involved. 相似文献
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In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity. 相似文献