共查询到19条相似文献,搜索用时 88 毫秒
1.
Chun Su Tao Jiang Qi-he TangDepartment of Statistics Finance University of Science Technology of China Hefei 《应用数学学报(英文版)》2002,18(4):675-680
Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities (?)(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model. 相似文献
2.
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
3.
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
4.
Tao Jiang 《高校应用数学学报(英文版)》2010,25(2):209-216
Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references. 相似文献
5.
In this paper,we study the smoothness of certain functions in two kinds of risk models with a barrier dividend strategy.Mainly using technique from the piecewise deterministic Markov processes theory,we prove that the function is continuously differentiable in the first risk model.Using the weak infinitesimal generator method of Markov processes,we prove that the function is twice continuously differentiable in the second risk model.Intego-differential equations satisfied by them are derived. 相似文献
6.
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes. 相似文献
7.
In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained. 相似文献
8.
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
9.
Ruin Probabilities under a Markovian
Risk Model 总被引:5,自引:0,他引:5
Han-xingWang Da-fanFang Mao-ningTang 《应用数学学报(英文版)》2003,19(4):621-630
In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)}t≥0 with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability ψ(0) and the bound for the convergence rate of the ruin probability ψ(u) are given by using the generalized renewal technique developed in this paper.Finally, we prove that the ruin probability ψ(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix(qij)i,j∈E such that qm = qml and qi=qi(i 1), 1≤i≤m-1. 相似文献
10.
Li Wei 《应用数学学报(英文版)》2012,28(1):31-38
This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field. 相似文献
11.
考虑常数利率情形下的延迟更新风险过程.得到了该延迟更新风险模型下的Gerber-Shiu期望折现罚金函数的表达式,并得到了常数利率下的一种特殊的延迟更新风险模型的破产概率的显示表达式. 相似文献
12.
In this paper we consider the discrete time stationary renewal risk model. We express the Gerber-Shiu discounted penalty function in the stationary renewal risk model in terms of the corresponding Gerber-Shiu function in the ordinary model. In particular, we obtain a defective renewal equation for the probability generating function of ruin time. The solution of the renewal equation is then given. The explicit formulas for the discounted survival distribution of the deficit at ruin are also derived. 相似文献
13.
本文考虑了一类特殊的延迟更新风险模型发生第一次索赔的时间服从指数分布的延迟更新风险模型.在这样的条件下,利用Gerber- Shiu贴现罚函数推导出了保险公司的破产概率. 相似文献
14.
In this paper, we investigate a renewal risk model in which the distribution of the interclaim times is a mixture of two Erlang
distributions. First, the Laplace transform and the defective renewal equation for the Gerber-Shiu function are derived. Then,
two asymptotic results for the Laplace transform of the time of ruin are given when the initial surplus tends to infinity
for the light-tailed claims and heavy-tailed claims, respectively. Finally, an explicit expression for the Gerber-Shiu function
is given. 相似文献
15.
In this paper, an Erlang(2) risk model with time-dependent
claims is studied under a multi-layer dividend strategy. First, some piecewise
integro-differential equations with certain boundary conditions for the Gerber-Shiu
function are derived. Then, applying these results, some defective renewal equations
and explicit expressions for the Gerber-Shiu function are obtained when the joint
density of the inter-claim time and claim size belongs to the rational family. 相似文献
16.
17.
本文考虑复合二项风险模型破产概率问题,首先通过研究Gerber-Shiu折现惩罚函数,运用概率论的分析方法得到了其所满足的瑕疵更新方程,再结合离散更新方程理论研究了其渐近性质,最后,运用概率母函数的方法得到了与经典的Gramer-Lundberg模型类似的破产概率Pollazek-Khinchin公式. 相似文献
18.
19.
In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided. 相似文献