Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.

Optimal Dividend Problem for a Compound Poisson Risk Model

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy. Moreover, two conjectures are proposed.

Dividend Payments with a Hybrid Strategy in the Compound Poisson Risk Model

In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are paid at a constant rate whenever the modified surplus is in a interval;the premium income no longer goes into the surplus but is paid out as dividends whenever the modified surplus exceeds the upper bound of the interval, otherwise no dividends are paid. Integro-differential equations with boundary conditions satisfied by the expected total discounted dividends until ruin are derived;for example, closed-form solutions are given when claims are exponentially distributed. Accordingly, the moments and moment-generating functions of total discounted dividends until ruin are considered. Finally, the Gerber-Shiu function and Laplace transform of the ruin time are discussed.

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.

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.

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.

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.

应急志愿组织之社会公权力的生成逻辑及其实现路径

应急志愿组织在实践中产生的乱象和争议,是其权责界限模糊导致的必然后果,有必要在法治层面完成应急志愿组织社会公权力构建,将其活动予以规范化、制度化。应急志愿组织之社会公权力生成的固有权模式、国家授权模式和契约论模式存在局限性,应从国家和社会共同在场的治理结构出发,以社会的自发构建和经国家承认并通过法律加以规范的授权模式为基础构建应急志愿组织之社会公权力。通过国家层面制度结构的赋权和社会层面社会信任的构建,实现对应急志愿组织的“复合授权”,使其更加规范有序地参与到应急治理体系之中。

非均质场地土壤VOCs通量衰减预测与风险评估

为反映实际场地源强或挥发通量的衰减对室内风险的影响,以某挥发性有机污染场地为例,在原有Jury模型基础上增加了建筑物底板及场地地层垂向异质性对传输通量的影响作用,比较了J&E模型与Jury模型在预测挥发通量,室内空气浓度、健康风险评估结果的差异及影响因素.结果表明:J&E模型预测进入室内的苯通量恒定,与实际场地存在源衰减不符.Jury模型可反映源通量衰减、包气带土壤和建筑底板的阻滞对室内浓度及风险的影响;Jury模型中的暴露区间设定是影响风险水平的关键因素.源形成初期,即T1情景下,暴露期只有两个点位超出可接受风险水平;中期T2情景下,4个点位超出风险可接受水平,后期T3情景下,7个点位超出风险可接受水平,而J&E模型为恒定源,不同时期均为7个点位超标.总体而言,Jury模型考虑了污染源衰减及上方覆盖土壤的阻滞作用,相对J&E模型更为合理.

Large deviations for generalized compound Poisson risk models and its bankruptcy moments

We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.

考虑不确定性的复合灾害避难疏散风险评估模型

为解决地震-暴雨典型复合灾害情景下避难疏散的不确定性,开展避难疏散风险评估研究。首先,基于我国避难疏散体系规划特征,提出地震暴雨复合灾害下城市避难疏散风险控制目标;其次,考虑避难疏散时间的不确定性,结合地震-暴雨复合灾害避难疏散特点,建立地震-暴雨复合灾害下城市道路通行能力快速评估模型;然后,考虑不同避难需求点风险接受程度的不确定性,提出基于城市规划用地特征的可接受风险水平系数;最后,考虑以上避难疏散过程的不确定性特征,采用优化算法计算最大覆盖应急设施选址决策模型,构建基于地震-暴雨复合灾害避难疏散风险评估模型,并以某北方城市防灾疏散责任区为实证对象,探讨多风险控制目标与多规划方案组合下的风险情况,提出该防灾疏散责任区的最小疏散风险避难场所规划方案。结果表明:该模型能更为实际地评估地震-暴雨复合灾害情景下避难疏散风险,实现不确定因素的量化分析,达到风险评估和空间规划的有效衔接。

障碍分红风险模型下的破产赤字折现密度函数的统计估计

本文研究了带有障碍分红策略的复合泊松风险模型下的破产赤字折现密度函数的统计估计.在索赔次数过程的泊松强度和个人索赔大小的密度函数均未知的情况下,我们运用COS方法构造了估计值,并且推导出了估计值的一致性.此外,在样本量有限情况下,我们提供的仿真结果验证了此统计估计方法的有效性.

Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models

In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.

The Gerber-Shiu Discounted Penalty Function for a Compound Binomial Risk Model with By-claims

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.

The Optimal Dividend Barrier in the Perturbed Compound Poisson Risk Model with Randomized Observation Time

This paper considers the dividend problems in the perturbed compound Poisson risk model.Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend.In this paper,integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived.When the claim is exponentially distributed,explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained.Finally,the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.

Some Large Deviation Results for Generalized Compound Binomial Risk Models

This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n ≥ 0} is a binomial process with a parameter p ∈ (0,1) and independent of {Xn,n ≥ 1}; {M(n),n ≥ 0} is a Poisson process with intensity λ > 0, Sn = ΣNn i=1 Xi-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.

随机利率下带干扰的双复合Poisson-Geometric过程双险种风险模型的破产概率研究

随着保险公司业务不断扩张和实际情况的日益复杂化,经典风险模型已经不能准确描述保险营运的实际过程;本文在已有模型的基础上将随机利率和干扰因素融入模型中,将模型推广为保费过程和索赔过程均为复合Poisson-Geometric风险模型,利用期望方法和切比雪夫不等式得到该风险模型的调节系数、破产概率表达式和Lundberg上界。

RBCA和Csoil模型在挥发性有机物污染场地健康风险评价中的应用比较

应用美国的RBCA模型和荷兰的Csoil模型对某挥发性有机物污染场地中的2种主要污染物1,2-二氯丙烷和1,2-二氯乙烷进行健康风险评价。结果表明,2种模型计算出的健康风险基本一致,除14号采样点存在潜在的健康风险外,其余各采样点的健康风险均在可接受的范围内。由土壤污染引起的各暴露途径中,直接经口摄入途径引起的健康风险最大,占65%以上;皮肤接触途径次之;呼吸摄入途径最小。在呼吸暴露途径中,室内挥发暴露明显比室外挥发暴露的健康风险大。Csoil模型计算出的所有采样点由地下水暴露途径引起的健康风险都超过土壤,说明由地下水暴露引起的健康风险不容忽视。RBCA模型在考虑地下水暴露途径时仅考虑了饮水摄入这一途径,与RBCA模型相比,Csoil模型在进行健康风险评价时特别考虑了洗澡暴露途径,对于地下水受到污染的场地来说,Csoil模型考虑得更全面,使用Csoil模型进行健康风险评价更具有针对性。

双复合Poisson风险模型

研究了保费收取过程是复合Po isson过程,索赔总额是复合Po isson过程的风险模型,给出了不破产概率的积分表示,以及在特殊情况下不破产概率的具体表达式,并用鞅方法得出了破产概率满足的Lundberg不等式和一般公式.