带干扰复合泊松模型下对调整系数的新研究(英文)

本文研究了带干扰复合泊松模型中采用成数再保与超额损失再保险混合策略时作为自留额水平函数的调整系数.我们按照原始条款计算成数再保费,按照期望值保费原则计算超额损失再保费,这样得到了调整系数是超额损失自留额极限的单峰函数的结论.本文最后部分给出了有限时间破产概率的上界.     

带干扰的相依双险种最优再保险

研究一类带干扰的理赔相依的双险种风险模型,其中两险种分别采取成数再保险和超额损失再保险.在期望保费计算原理下,利用调节系数最大化得到成数再保险及超额损失再保险的最优自留水平.     

双险种最优再保险策略

本文对双险种风险模型,在一险种采取比例再保险,另一险种采取超出损失再保险策略下,得到调节系数与再保险自留水平之间的函数关系式,在理赔额为指数分布和Erlang(2)分布的条件下,得到最优比例再保险和超出损失再保险的自留水平,以及调节系数最大值。     

多险种风险模型的再保险

本文在考虑保险公司实际经营过程的基础上,建立了一个索赔到达为齐次Poisson过程且含有随机干扰项的多险种风险模型,分别讨论了其在比例再保险和超额再保险两种情况下调节系数R的上下界,得到索赔额服从指数分布时调节系数R与比例再保险比例系数α,以及调节系数R与超额再保险的免赔额M的关系式,并分别给出算例,得出和经典风险模型再保险一致的结论.     

基于追溯保费原理的最优再保险策略

追溯保费是一种依赖于保单期保险人实际损失的保费厘定计划,是对过去已经发生的损失进行承保的保险方式.本文将追溯保费应用于再保险模型中,当最优准则选为最小化风险调整值而风险资本用TVaR来度量时,得到的最优分保函数形式为停止损失再保险.进而,研究了最优停止损失再保险中最优自留额的求解算法.最后,假设损失服从指数分布、Pareto分布和Gamma分布等情形,利用数值举例的方法研究了税租乘数T和安全负荷系数ρ对最优自留额和最小风险调整值的影响.结果表明,当其他参数一定时, T增大,最优自留额增大而最小风险调整值减小;而其他参数一定时,最优自留额和最小风险调整值都会随着ρ的增大而增大.     

投资影响下的再保险策略

本文研究了投资影响下的再保险策略,利用有关的线性正倒向随机微分方程,获得投资影响下再保险的自留比例或自留额的计算式子.     

基于投资的再保险定价模型

从系统的观点出发,把公司的赔付情况与投资收益相接合,对比例再保险与超额损失再保险,建立了在投资影响下的带跳的再保险模型,给出了基于投资的再保险定价公式,为公司厘订再保险费提供了新的方法.     

基于夏普比率的最优再保险策略

当保险公司承保巨灾风险时,通过再保险转移风险是非常必要的。再保险是保险人将其承保业务的一部分转移给再保险人的行为,而再保险业务中核心是最优再保险策略问题,即以何种形式分保以及具体分保的额度。本文引入基金业中风险管理和绩效评估等方面常用的指标-夏普比率,构建了基于该指标的再保险策略风险模型.对于分保业务中常见的两种形式:成数再保险和止损再保险,文章通过分析得出使得保险人夏普比率最大化的风险自留比率和风险自留额度。基于夏普比例对最优再保险策略的研究可以为保险公司的再保险业务提供决策依据。     

隐含风险中性分布在巨灾超额损失再保险定价中的应用

通过与标的风险相关的期权市场估计出隐含变换系数,然后以Esscher变换为工具,将巨灾损失统计分布风险中性化,从而对以该非交易风险为标的的巨灾超额损失再保险进行定价.同时,从期权定价的角度,结合Weibull极值分布和超额损失再保险的特点,给出了巨灾超额损失再保险定价的闭型表达式.     

最优比例与超额损失组合再保险下的破产概率

本文站在保险人的立场上,讨论了保险公司的最优组合再保险问题.通过纯粹比例再保险,纯粹超额损失再保险,或者这两类再保险的组合方式,把保险公司的部分风险分担出去.在最大化调节系数的最优准则下,我们得出了布朗运动模型和复合Poisson模型中最优值的显示表达,并且给出了复合Poisson模型中最优策略下破产概率的最小指数上界.我们还得出结论:在一定的条件下,总存在一种纯粹超额损失再保险策略比任何一类组合再保险策略都要好.最后,通过一些数例和图表来进一步说明我们在文中所获得的结论.     

最优成数再保险决策模型研究

根据期望值计算原理下,给出了由n种索赔次数相关的相关险种构成的总体最优成数再保险函数.     

Measuring the effects of reinsurance by the adjustment coefficient

In this paper we consider the optimal levels of reinsurance in cases where the cedent has a choice between a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The optimality criterion that we use is that the insurer's adjustment coefficient should be maximized, subject or not to a constraint on the insurer's expected net profit. The solution is given, assuming that the claims have a compound Poisson distribution, that the quota-share premium is calculated on a proportional basis with a commission payment and that the excess of loss reinsurance premium is calculated according to the expected value principle.     

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??Motivated by[1] and [2], we study in this paper the optimal (from the insurer's point of view) reinsurance problem when risk is measured by a general risk measure, namely the GlueVaR distortion risk measures which is firstly proposed by [3].Suppose an insurer is exposed to the risk and decides to buy a reinsurance contract written on the total claim amounts basis, i.e. the reinsurer covers and the cedent covers . In addition, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the reinsurance premium, ( is the safety loading), under the expectation premium principle. Based on a technique used in [2], this paper derives the optimal ceded loss functions in a class of increasing convex ceded loss functions. It turns out that the optimal ceded loss function is of stop-loss type.     

关于停止损失再保险的调节系数最大化问题

停止损失再保险作为一种再保险方式,在具有相同保费的前提下,能使保险人的期望效用最大,并能使其自留风险方差最小.另外在保费和费率相等的前提下,停止损失再保险的调节系数不可能比其他再保险方式的调节系数小.本论文在此基础上作了相应推广,讨论了在保费相等的前提下,停止损失再保险的费率满足时,其调节系数不小于其他再保险方式的调节系数.     

Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria

This paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer.Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.     

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Based on the default risk effect of reinsurance company for reinsurer, this paper studies the optimal reinsurance strategy by VaR optimality criterion. In a reinsurance contract, reinsurance company will charge the number of premium to undertake part of the insurer's loss. However, if the reinsurance company's commitment exceeds its solvency, the default risk will occur. In order to avoid the default risk and minimize the total risk of the insurance company, the paper introduces Wang's premium principle to obtain the optimal reinsurance policy under VaR risk measure. Some numerical examples are given to illustrate these results.