Pooling,pricing and trading of risks

Exchange of risks is considered here as a transferable-utility, cooperative game, featuring risk averse players. Like in competitive equilibrium, a core solution is determined by shadow prices on state-dependent claims. And like in finance, no risk can properly be priced merely in terms of its marginal distribution. Pricing rather depends on the pooled risk and on the convolution of individual preferences. The paper elaborates on these features, placing emphasis on the role of prices and incompleteness. Some novelties come by bringing questions about existence, computation and uniqueness of solutions to revolve around standard Lagrangian duality. Especially outlined is how repeated bilateral trade may bring about a price-supported core allocation.     

Applying simulation optimization to the asset allocation of a property–casualty insurer

Proper asset allocations are vital for property–casualty insurers to be competitive and solvent. Theories of finance offer little practical guidance in constructing such asset allocations however. This research integrates simulation models with a newly developed evolutionary algorithm for the multi-period asset allocation problem of a property–casualty insurer. We first construct a simulation model to simulate operations of a property–casualty insurer. Then we develop multi-phase evolution strategies (MPES) to be used with the simulation model to search for promising asset allocations for the insurer. A thorough experiment is conducted to evaluate the performance of our simulation optimization approach. Computational results show that MPES is an effective search algorithm. It dominates the grid search method by a significant margin. The re-allocation strategy resulting from MPES outperforms re-balancing strategies significantly. This research further demonstrates that the simulation optimization approach can be used to study economic issues related to multi-period asset allocation problems in practical settings.     

保险企业偿付能力的监控

本讨论保险公司偿付能力监控指标的构成,并针对我国目前保险公司的现状提出用多元统计控制方法和指标加权平均法对保险公司偿付能力进行监控,最后,以一例说明其实际应用。     

Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladder reserving models

This is the first study to derive closed-form analytical expressions for multi-year non-life insurance risk in the chain ladder model. Extending on previous research on the additive reserving model, we define multi-year risk via prediction errors of multi-year claims development results including both observed and future accident years. A resampling argument and a first-order Taylor approximation address the quantification of estimation errors and multiplicative dependencies in the chain ladder framework, respectively. From our generalized multi-year approach, we deduce estimators for reserve and premium risks in multi-year view and their implicit correlation. We reproduce well-known results from literature for the special cases of one-year and ultimo view. Further, we comment on how to obtain estimators for generalized versions of the chain ladder method. A case study demonstrates the applicability of our analytical formulae.     

A computational model of a bonus-malus system with a variable trend

The paper considers a model of a bonus-malus system with a variable trend in the case of a three-parameter gamma distribution. The parameters of the distribution and the value of the trend are selected based on statistical data. The indexes of the bonus-malus system are obtained.     

基本养老保险的定量分析

从宏观经济的动态观点,提出了多层次的养老金给付体系,有效地克服了传统给付模型的不足.     

随机利率下的终身寿险

本文给出 了 在 随机 利率下,终身寿 险的纯保费和 纯保 费责任准备金的计算方 法.并讨论了与之 有关的其他精算 问题.     

Optimal insurance design in the presence of exclusion clauses

The present work studies the design of an optimal insurance policy from the perspective of an insured, where the insurable loss is mutually exclusive from another loss that is denied in the insurance coverage. To reduce ex post moral hazard, we assume that both the insured and the insurer would pay more for a larger realization of the insurable loss. When the insurance premium principle preserves the convex order, we show that any admissible insurance contract is suboptimal to a two-layer insurance policy under the criterion of minimizing the insured’s total risk exposure quantified by value at risk, tail value at risk or an expectile. The form of optimal insurance can be further simplified to be one-layer by imposing an additional weak condition on the premium principle. Finally, we use Wang’s premium principle and the expected value premium principle to illustrate the applicability of our results, and find that optimal insurance solutions are affected not only by the size of the excluded loss but also by the risk measure chosen to quantify the insured’s risk exposure.     

基于VaR的科技保险风险补偿问题研究

VaR(Value at Risk)是金融企业进行全面风险管理的有效工具,是保险公司“偿二代(C-ROSS)”量化资本要求采用的方法。本文利用VaR工具,在委托代理框架下,研究了科技保险风险补偿合同问题,阐述了科技保险风险补偿的理论依据。在对称信息与非对称信息情形下,获得了风险补偿合同的闭式解。本文结果显示,合同中固定补偿将起主导作用,最优边际补偿系数可正可负,且随保险公司置信水平增加而递减。