Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model 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.

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.

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.

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.

Precise large deviation result for heavy-tailed random sums and applications to risk theory

The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.

Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims

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.

Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk models

Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al.(2010), the price process of the investment portfolio is described as a geometric L′evy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al.(2010).

高比例新能源电力系统调节资源灵活性不足风险分析

高比例新能源接入电力系统带来了显著的波动性和不确定性,电力系统面临灵活性不足的运行风险。不确定状态下灵活性不足风险评判对控制电力系统运行风险水平、评价规划方案的性能优劣具有重要意义。研究新能源电力系统调节资源灵活性不足风险量化评估方法,提出了新能源电力系统调节资源灵活性不足风险评价指标体系。首先,基于核密度估计与序优化理论,提出源荷不确定性数据驱动建模方法;为提高电力系统源荷样本数据的充裕度,提出基于云模型的电力系统小概率风险样本集重构方法,实现训练样本的无成本、灵活获取;然后,从爬坡能力和调节深度两方面提出新能源电力系统调节资源灵活性不足的风险量化评估方法。最后,算例分析验证了所提方法的有效性和可行性。

电力系统风险规避投资模型及分布式求解策略

建立电源、电网、柔性负荷和储能的数学模型,引入条件风险价值度量可再生能源不确定性风险,建立互联电力系统“源-网-荷-储”协调规划模型。考虑各区域电力系统信息安全性和隐私性提出分布式求解策略,以区域间联络线为耦合变量将集中式优化模型解耦为分布式优化模型。将动态惩罚参数和预测校正策略整合到交替方向乘子算法提高收敛速度,通过算例仿真验证基于分布式优化的风险规避投资模型的有效性。

更新过程若干矩性质及其风险理论应用

更新过程作为一类重要的计数随机过程,在金融风险理论、可靠性理论等研究领域均具有广泛应用。本文从更新过程的均值函数更新函数有限证明出发,利用其证明思想,进一步研究了更新过程若干矩函数性质,包括任意阶矩函数、指数阶矩函数性质等。最后本文列举了更新过程矩函数性质在风险理论中的一个简单应用。

基于频域阻抗的新能源并网振荡风险评估方法

随着新能源装机规模不断增加,如何评估由其引发的系统次/超同步振荡风险是目前电网运行高度关注的重要问题。提出了一种基于频域阻抗的新能源并网振荡风险评估方法,首先利用系统各元件频域导纳模型形成网络节点导纳矩阵,实现对新能源场站并网点系统侧网络等效阻抗的计算,能准确反映电网结构特性以及网内其他设备的动态特性,然后结合新能源场站阻抗特性,通过阻抗分析评估新能源场站并网振荡风险。该方法采用电路节点分析法,算法易于实现,能够适应系统结构和运行方式变化,充分反映网侧动态元件的影响,可利用电网同步相量测量装置提供的结构和潮流数据对系统内新能源场站并网振荡风险进行评估分析。以某地区实际电力系统为研究对象,利用所提方法展开了次同步振荡风险评估,同时基于特征值法和时域仿真验证了评估结果的准确性和评估方法的有效性。

A Class of Delayed Renewal Risk Processes with a Threshold Dividend Strategy

This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.

基于可再生能源的配电网电力调度优化模型研究

为了降低线路损耗与运行越限风险,构建基于可再生能源的配电网电力调度优化模型。针对可再生能源的波动性,以最低线路损耗与运行越限风险为目标函数,以电压约束、储能功率约束、潮流约束、结构调整约束为约束条件,建立配电网电力调度优化模型,利用基于帝国分裂的帝国竞争算法求解电力调度优化模型,获取最低线路损耗与运行越限风险对应的电力调度策略。实验证明:该模型可有效完成配电网电力调度,降低线路损耗与运行越限风险,抑制电压波动;在不同可再生能源渗透率时,该模型也可有效完成配电电力调度,提升电能质量。

回归相依结构的次指数索赔加权和的精确大偏差

考虑一个更新风险模型,其符合一个m相依序列的半马尔可夫型的回归相依结构,即当前索赔时间依赖于固定数量的先前索赔,但独立于所有其他索赔。作为描述非寿险业务的一种实用手段,该结构放宽了索赔规模与间隔时间之间的独立性假设,为包括金融和保险在内的各种应用提供了合适的框架,并研究了具有回归相依结构的更新风险模型中次指数加权索赔和模型,并利用Bonferroni不等式和大数马尔科夫定律得出其精确大偏差,推广了现有文献结论。

基于改进领结模型的老旧小区改造项目风险管理探究

我国城市建设正在从“增量扩张”向“存量更新”转型,其中老旧小区改造已成为“十四五”规划中有关城市更新中的一项重要惠民举措,但老旧小区改造过程中存在诸多风险,一定程度上阻碍了城市更新的进程,故有必要系统地展开老旧小区改造项目风险识别、评价及管理相关研究。本文提出一种老旧小区改造风险管理方案,首先通过文献梳理及专家咨询较全面地归纳出当前老旧小区改造中潜在的风险因素;然后,构建老旧小区改造风险识别管理方法,即在老旧小区改造项目风险识别的基础上,采用Borda序值法对项目中风险因素的重要程度进行定量化排序,运用改进领结模型对涵盖重要风险因素的施工场景展开研究,分析施工过程中可能发生的事故,并设置预防和缓解屏障以降低事故发生概率和减轻后果影响。最后,以S市某老旧小区改造实际项目风险评价管理为研究案例,测试了本文构建的老旧小区改造风险识别与管理方法的有效性、可行性。

续贷限制对企业风险承担的影响——基于准自然实验的经验证据

当前新形势下,提升企业风险承担水平是疏通国内经济大循环的重要渠道。本文以2007年续贷政策变动为“准自然实验”,采用双重差分模型考察续贷政策变化对企业风险承担的影响。研究结果表明,续贷限制显著抑制了企业的风险承担。异质性分析表明,对于投资机会较多的企业和非国有企业来说,续贷政策收紧抑制其风险承担的效果更显著。机制检验表明,融资约束与现金持有在续贷限制对企业风险承担的负向影响中起链式中介作用。研究结论对改进银行续贷政策以促进企业风险承担具有启示意义。

Extension of Some Classical Results on Ruin Probability to Delayed Renewal Model

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.

更新风险模型和延迟更新风险模型中破产概率的若干结果

本文进一步研究更新风险模型和延迟更新风险模型中的破产概率ψ(χ),这里χ是保险公司的初始资本.在假定个体索赔分布是重尾的前提下,得到了与经典模型相一致的破产概率ψ(χ)的一个尾等价关系.