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在汽车保险的奖惩系统中加入免赔额,将有利于保证风险与保费的匹配,还可以减少小额损失带来的大量管理费用.本文应用马尔科夫最优化原理推广了汽车保险的最优索赔策略模型.根据我国现行的机动车辆保险条款,得到了加入免赔额时的最优索赔策略. 相似文献
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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. 相似文献
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为了避免由高理赔额造成的违约,保险公司通常通过签订再保合约将一部分风险转移给再保险公司.近年来对最优再保策略的研究着眼于最小化自留损失的方差,保险公司总风险的value-at-risk或conditional tail expectation.本文研究了在expected shortfall准则下的再保策略.我们给出了最优的增凸转移损失函数,并分别讨论了有无保费限制的情形. 相似文献
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研究保险公司用超额索赔再保险最小化其有限时间破产概率的问题,用鞅方法得到有限时间破产概率的上界以及保险公司的最优再保险自留额. 相似文献
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本文推广了Centeno[1],何树红[2],张茂军[3]的模型,研究带干扰的常利率超额再保险风险模型。首先用鞅方法求得其调节函数,进而证明Lundberg不等式,给出有限时间破产概率上界,并讨论最优自留额的确定。 相似文献
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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. 相似文献
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Weiwei Zhuang 《Insurance: Mathematics and Economics》2009,44(3):409-414
In the literature, orderings of optimal allocations of policy limits and deductibles were established by maximizing the expected utility of wealth of the policyholder. In this paper, by applying the bivariate characterizations of stochastic ordering relations, we reconsider the same model and derive some new refined results on orderings of optimal allocations of policy limits and deductibles with respect to the family of distortion risk measures from the viewpoint of the policyholder. Both loss severities and loss frequencies are considered. Special attention is given to the optimization criteria of the family of distortion risk measures with concave distortions and with only increasing distortions. Most of the results presented in this paper can be applied to some particular distortion risk measures. The results complement and extend the main results in Cheung [Cheung, K.C., 2007. Optimal allocation of policy limits and deductibles. Insurance: Mathematics and Economics 41, 291-382] and Hua and Cheung [Hua, L., Cheung, K.C., 2008a. Stochastic orders of scalar products with applications. Insurance: Mathematics and Economics 42, 865-872]. 相似文献
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Worst allocations of policy limits and deductibles 总被引:1,自引:1,他引:0
In the literature, orderings of optimal allocations of policy limits and deductibles were established with respect to a policyholder’s preference. However, from the viewpoint of an insurer, the orderings are not enough for the purpose of pricing. In this paper, by applying the equivalent utility premium principle, we study worst allocations of policy limits and deductibles for an insurer, which give rise to the maximum fair premiums. Closed-form solutions are derived. Then we present a result concerning the optimality in a general risk-sharing scheme, by which we obtain optimal allocations for policyholders directly from worst allocations for an insurer. Several results in Cheung [Cheung, K.C., 2007. Optimal allocation of policy limits and deductibles. Insurance Math. Econom. 41, 382–391] are generalized here. 相似文献
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In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma [Ma, C., 2000. Convex orders for linear combinations of random variables. J. Statist. Plann. Inference 84, 11-25], we first obtain more general conditions under which linear combinations of random variables can be ordered in the increasing convex order. As an application of this result, we consider the scalar product of two random vectors which separates the severity effect and the frequency effect in the study of the optimal allocation of policy limits and deductibles. Finally, we obtain the ordering of the optimal allocation of policy limits and deductibles when the dependence structure of the losses is unknown. This application is a further study of Cheung [Cheung, K.C., 2007. Optimal allocation of policy limits and deductibles. Insurance: Math. Econom. 41, 382-391]. 相似文献
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Recently, Escudero and Ortega (Insur. Math. Econ. 43:255–262, 2008) have considered an extension of the largest claims reinsurance with arbitrary random retention levels. They have analyzed
the effect of some dependencies on the Laplace transform of the retained total claim amount. In this note, we study how dependencies
influence the variability of the retained and the reinsured total claim amount, under excess-loss and stop-loss reinsurance
policies, with stochastic retention levels. Stochastic directional convexity properties, variability orderings, and bounds
for the retained and the reinsured total risk are given. Some examples on the calculation of bounds for stop-loss premiums
(i.e., the expected value of the reinsured total risk under this treaty) and for net premiums for the cedent company under
excess-loss, and complementary results on convex comparisons of discounted values of benefits for the insurer from a portfolio
with risks having random policy limits (deductibles) are derived.
相似文献
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The insurer usually solicits the insured through granting a certain amount of deductible to multiple risks according to his/her own will. Due to the nonlinear nature of the concerned optimization problem, in the literature on the optimal allocations of deductibles researchers usually assume independence or comonotonicity among concerned risks and ignore the impact due to frequency. In this study we build two sufficient conditions for the decreasing optimal allocation of deductibles, relaxing the stochastic arrangement increasing or right tail weakly stochastic arrangement increasing discount factors in Cai and Wei (2014, Theorems 6.3 and 6.6) to the conditionally upper orthant arrangement increasing or weak conditionally upper orthant arrangement increasing frequencies. 相似文献
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Fengxia Hu 《Journal of Computational and Applied Mathematics》2010,234(10):2953-2961
By maximizing the expected utility, we study the optimal allocation of policy limits and deductibles from the viewpoint of a policyholder, where the dependence structure of losses is unknown. In Cheung (2007) [K.C. Cheung, Optimal allocation of policy limits and deductibles, Insurance: Mathematics and Economics 41 (2007) 382-391], the author had considered similar problems. He supposed that a policyholder was exposed to n random losses, and the losses were general risks there, i.e., the loss on each policy was just a random variable. In this paper, the model is extended in two directions. On one hand, we assume that n policies of the n losses are effected by random environments. For each policy, the loss under a fixed environment is characterized by a random variable, so the loss on each policy is a mixture of some fundamental random variables. On the other hand, loss frequencies, which are stochastic, are also considered. Therefore, the whole model is equipped with mixture risks and discount factors. Finally, we get the orderings of the optimal allocations of policy limits and deductibles. Our conclusions also extend the main results in Hua and Cheung (2008) [L. Hua, K.C. Cheung, Stochastic orders of scalar products with applications, Insurance: Mathematics and Economics 42 (2008) 865-872]. 相似文献
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《Insurance: Mathematics and Economics》2008,42(3):382-391
In this paper, we study the problems of optimal allocation of policy limits and deductibles. Several objective functions are considered: maximizing the expected utility of wealth assuming the losses are independent, minimizing the expected total retained loss and maximizing the expected utility of wealth when the dependence structure is unknown. Orderings of the optimal allocations are obtained. 相似文献
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Ka Chun Cheung 《Insurance: Mathematics and Economics》2007,41(3):382-391
In this paper, we study the problems of optimal allocation of policy limits and deductibles. Several objective functions are considered: maximizing the expected utility of wealth assuming the losses are independent, minimizing the expected total retained loss and maximizing the expected utility of wealth when the dependence structure is unknown. Orderings of the optimal allocations are obtained. 相似文献
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With the assumption of Archimedean copula for the occurrence frequencies of the risks covered by an insurance policy, this note further investigates the allocation problem of upper limits and deductibles addressed in Hua and Cheung (2008a). Sufficient conditions for a risk averse policyholder to well allocate the upper limits and the deductibles are built, respectively. 相似文献
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《Insurance: Mathematics and Economics》2012,50(3):418-428
The present work studies the optimal insurance policy offered by an insurer adopting a proportional premium principle to an insured whose decision-making behavior is modeled by Kahneman and Tversky’s Cumulative Prospect Theory with convex probability distortions. We show that, under a fixed premium rate, the optimal insurance policy is a generalized insurance layer (that is, either an insurance layer or a stop–loss insurance). This optimal insurance decision problem is resolved by first converting it into three different sub-problems similar to those in Jin and Zhou (2008); however, as we now demand a more regular optimal solution, a completely different approach has been developed to tackle them. When the premium is regarded as a decision variable and there is no risk loading, the optimal indemnity schedule in this form has no deductibles but a cap; further results also suggests that the deductible amount will be reduced if the risk loading is decreased. As a whole, our paper provides a theoretical explanation for the popularity of limited coverage insurance policies in the market as observed by many socio-economists, which serves as a mathematical bridge between behavioral finance and actuarial science. 相似文献