保险赔付中的最优对冲策略

本文对带有付费过程$A_t$的保险公司在金融市场$(S_t,Q_t,B_t)$上通过购买股票$S_t$、兑换外币$Q_t$以及购买无风险资产$B_t$的投资过程而采取的最优投资策略, 使保险公司所面临的风险最小进行探讨. 利用Galtchouk-Kunita-Watanabe分解定理将风险表达式重新表达, 从而找到保险公司所能采取的风险最小的最优对冲策略. 文中举出一个具有现实性意义的例子将文章的重要结论加以应用, 使本文更具有应用价值.     

常利率下保费随马氏环境变化的风险模型的破产概率

破产概率受保费变化影响,保费随着准备金变化,在本文中考虑带有利率的风险模型;其索赔发生是Cox过程.     

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.     

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.     

理赔额与理赔间隔相依的风险模型的若干结论

本文研究了一类具有相依结构的风险模型.利用无穷小方法,得到了Gerber-Shiu罚金折现期望函数所满足的积分-微分方程,给出了破产时刻,破产赤字及破产前瞬时盈余的拉普拉斯变换的积分-微分方程的应用.最后,在具有常数红利边界下的同-风险模型中,分析了红利支付的期望现值.     

随机利率下的风险模型

考虑随机利率情形下关于风险损失(或赔款)的随机风险模型.当随机利率取一般的独立增量过程时,得到了总索赔额精算现值的各阶矩.特别地,当独立增量过程为Wiener过程,损失分布为Pareto分布的情形下,给出了总索赔额精算现值各阶矩的具体表达式.     

最优奖惩系统的构建与评价——基于索赔次数与赔款金额的综合视角

在商业车险中,奖惩系统是一种重要的后验费率调整机制,其基本原理是根据保单的历史索赔信息对续期保费进行调整。常见的奖惩系统仅考虑保单的历史索赔次数信息,但却忽视了赔款金额的影响,这可能会造成产品费率与其实际风险水平不匹配。本文综合考虑保单的索赔次数与赔款金额的信息,利用贝叶斯方法构建了新的最优奖惩系统,并运用极大似然法对模型参数进行估计。本文以我国商业车险中的一组索赔数据为例,进行实证研究。结果表明,对于不同赔款金额的保单,本文所构建的奖惩系统可通过不同的惩罚系数对其续期保费进行调整,从而有效提高后验费率厘定的准确性。     

一类相依两险种风险模型的分类破产概率

本文考虑文[1]中引入的一类索赔达到计数过程相关的两险种风险模型.利用更新方法,获得了该风险模型的分类破产概率的渐进结果,并给出了指数索赔情形下分类破产概率的表达式,从而改进了文[1]中的相关结果.     

风险非同质时索赔次数的分布拟合及其EM算法

本文运用EM算法,对于风险非同质时索赔次数的分布,分别给出了离散型多元风险模型,混合两伽玛模型参数的极大似然估计的迭代公式,并将其应用到一个实际问题中去,效果较好。     

EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.