共查询到19条相似文献,搜索用时 187 毫秒
1.
Ying-hui Dong 《高校应用数学学报(英文版)》2009,24(1):14-20
This paper studies a Sparre Andersen negative risk sums model in which the distribution of "interclaim" time is that of a sum of n independent exponential random variables. Thus, the Erlang(n) model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ(u) are given. For some special cases a closed-form expression for ψ(u) is derived. 相似文献
2.
This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ (0) is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin. 相似文献
3.
LiWei Hai-liangYang 《应用数学学报(英文版)》2004,20(3):495-506
In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results. 相似文献
4.
Sun Chuanguang 《高校应用数学学报(英文版)》2007,22(1):109-118
In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given. 相似文献
5.
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
6.
Li Wei 《应用数学学报(英文版)》2008,24(4):649-654
Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation. 相似文献
7.
In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process (PDMP). We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process. 相似文献
8.
A recursive formula of the Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims is obtained. In the discount-free case, an explicit formula is given. Utilizing such an explicit expression, we derive some useful insurance quantities, including the ruin probability, the density of the deficit at ruin, the joint density of the surplus immediately before ruin and the deficit at ruin, and the density of the claim causing ruin. 相似文献
9.
In this paper,we consider a generalization of the classical ruin model,where the income is random and the distribution of the time between two claim occurrences depends on the previous claim size.This model is more appropriate than the classical ruin model.Explicit expression for the generating function of the Gerber-Shiu expected discounted penalty function are derived.A similar model is discussed.Finally,the result are showed by two examples. 相似文献
10.
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
11.
考虑一类具有Poisson过程和Erlang(n)过程的风险模型的破产问题,该模型中保险公司具有两类保险,每类保险的理赔次数过程都是Poisson过程与一个共同的Erlang(n)过程的和.针对这类理赔相关的风险模型,就利息力为常数的情形得到破产时刻罚金折现期望的积分—微分方程. 相似文献
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13.
高珊 《数学的实践与认识》2008,38(22)
研究了一类相依的双险种风险模型,其中第一类险种的索赔到达计数过程为E lang(2)过程,第二类险种的索赔到达计数过程为其p-稀疏过程.首先通过更新论证的方法得到罚金折现期望满足的积分-微分方程,然后推导拉普拉斯变换的表达式,并就索赔额服从指数分布的情形得到了罚金折现期望的精确表达式. 相似文献
14.
Gordon E. Willmot 《Insurance: Mathematics and Economics》2007,41(1):17-31
The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shown to be a mixture of residual lifetime claim severity distributions, which results in an invariance property satisfied by a large class of claim amount models. The class of exponential claim size distributions is considered, and the Laplace transform of the (discounted) defective density of the surplus immediately prior to ruin is obtained. The mixed Erlang claim size class is also examined. The simplified defective renewal equation which results when the penalty function only involves the deficit is used to obtain moments of the discounted deficit. 相似文献
15.
将由布朗运动刻画的随机干扰项加入到Erlang(2)风险模型中,在模型中引入了由Gerber和Shiu定义的期望折现惩罚函数,并给出了这类模型的Gerber-Shiu函数所满足的积分微分方程. 相似文献
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本文主要研究了一类Sparre Andersen模型,其索赔时间间隔的分布为指数分布与Erlang(n) 分布的混合.得到了当初始资金u趋于无穷大时,破产概率ψ(u)的确切表达式和渐近表达式. 相似文献
19.
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