A Ruin Model with Random Income and Dependence between Claim Sizes and Claim Intervals

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.

A Ruin Model with Compound Poisson Income and Dependence Between Claim Sizes and Claim Intervals

We consider a ruin model with random income and dependence between claim sizes and claim intervals. In this paper, we extend the determinate premium income into a compound Poisson process and assume that the distribution of the time between two claim occurrences depends on the previous claim size.Given the premium size is exponentially distributed, the（Gerber-Shiu） discounted penalty functions is derived.Finally, we consider a similar model.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

A Local Asymptotic Behavior for Ruin Probability in the Renewal Risk Model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.

Comparison of Ruin Probabilities in Compound Poisson Risk Model

Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.

A Decomposition of the Ruin Probability for Risk Process with Vasicek Interest Rate

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.

On the Markov-dependent risk model with tax

In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems of integro-differential equations satisfied by the expected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov-dependent risk model without tax are established. The analytical solutions of the systems of integro-differential equations are also obtained by the iteration method.

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

A Joint Density Function in the Renewal Risk Model

In this paper, we consider a general expression for Ф（u, x, y）, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is O. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for Ф（u, x, y）. Finally, we give a numerical example to illustrate the application of these results.

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

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.

具有随机投资收益过程的风险模型有限时间破产概率的一致渐近估计

本文考虑一类利用càdlàg过程刻画保险盈余的随机投资收益,并利用二元上尾独立刻画保险索赔额之间相依结构的保险风险模型.一方面,本文提出条件(6),在此条件下得到该风险模型有限时间破产概率的一致渐近估计式.另一方面,考虑到条件(6)的普适性,本文发现很多重要的随机过程都满足条件(6),如Lévy过程,Vasicek模型,Cox-Ingersoll-Ross(CIR)模型和Heston模型.

活态流变:废墟与建筑遗产评估及再现

从汉口开埠到老城新生,原以废墟形式存在的建筑遗产逐渐复现在大众视野下。基于对废墟的审美经验与文化价值论,对其进行内在价值与可用性评估,选取武汉翟雅阁为研究对象,采用可利用性评估权重问卷,对相关数据进行采集、分析,再引入模糊层次分析法模型(F-AHP)与Critic赋权法对翟雅阁进行判断矩阵组合赋权,最后以云理论为基础构建建筑遗产评估模型,从中探求最小化遗产价值流失的方法策略与流程,活化利用、以古为新,冀借他山之石为启发相关建筑遗产保护的同类研究提供理论意义与现实价值。

期望保费准则下的最优再保险策略

再保险作为“保险的保险”,是一种有效的风险管理策略.在期望保费准则下,对成数再保险、停止损失再保险及两者的混合再保险的最优化问题进行研究.利用鞅方法得到了复合泊松风险模型中的有限时间破产概率上界,并证明了在最小化有限时间破产概率上界的指标下,停止损失再保险要优于两者的混合再保险.

随机投保费下多险种破产模型的研究

用单一险种风险模型来描述保险公司的经营存在的局限性,建立了考虑运行费用的带有干扰项及随机保费的多险种破产模型,经推理论证得到了5个定理,给出了最终破产概率及一个上界,拓展了经典破产模型的应用范围.

随机保费率下带干扰风险模型的破产概率

考虑了保险费收取率为随机变量且含随机干扰因素的风险模型,在更一般的情形下,得到了破产概率满足的一般公式和Lundberg不等式.并且,通过实例分析了破产概率与初始资本、保费额及理赔额之间的关系.

定期人寿保险的破产概率和调节系数

为了研究定期人寿保险中破产风险的问题,设计出一种T年期的定期人寿保险的险种.因为每个被保险人的死亡概率与年龄的大小密切相关,所以对所有的被保险人按照年龄进行分组,通过研究每个小组的破产模型,计算出破产概率,从而推导出破产模型的总破产概率.通过对风险破产理论知识的灵活运用,计算出本模型的调节系数,最后得到一个破产概率的上界.对于保险公司设计相应的财务预警系统,以及保险监管部门设计某些监管指标系统等问题有直接的参考和指导作用.

楠竹加筋复合锚杆内部界面黏结滑移模型

楠竹加筋复合锚杆已经应用于中国西北丝绸之路上留存的古代土遗址保护加固工程中。该锚杆截面积大,可以获得足够大的锚固力。针对现场拉拔试验中钢绞线从内黏结剂中拔出的破坏形式,设计了专门的试件及夹具,试验研究了钢绞线与内黏结剂间的力学行为。试验结果表明,钢绞线与内黏结剂的黏结滑移分为指数上升阶段、软化下降阶段和残余应力阶段3个阶段,可以用简化模型和精确模型描述。试验还表明,钢绞线与内黏结剂接触界面上应力分布不均匀,靠近加载端的应力较大,且有应力峰,应力峰随荷载的逐渐增大向远离加载端的方向移动;钢绞线与内黏结剂间平均剪切应力随锚杆的长度增大呈指数衰减。通过理论分析,给出了界面黏结滑移微分方程及相关曲线,结果表明,钢绞线轴力及界面相对滑移沿钢绞线均呈不均匀分布,且随着距加载端的距离增加其值急剧下降,该规律可以指导锚杆设计及工程应用。

对于大额索赔的平衡更新模型的破产概率

本文研究平衡更新风险模型的破产概率ψ（x）,这里x为保险公司初始的资本金.在假定索赔额服从重尾分布的条件下,给出了当x→∞时;ψ（x）的尾等价关系,所得结果与经典的Cramer-Lundbeng模型下的结论完全一致.