寿险营销的创新战略——数据库营销

客户是企业的生命,也是企业唯一诉求的目标.开拓新客户,服务老客户,培养长期的忠诚的客户群,这是企业的价值所在.目前,寿险营销的核心问题就是客户问题.以代理人为主体的行销过程中,存在着准客户积累不足、新客户开拓不足、老客户留存不足、忠诚客户沉淀不足的问题.本文提出了数据库营销的创新战略,从根本上解决了服务客户时的"找不到...     

Extremes on the discounted aggregate claims in a time dependent risk model

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model.     

On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

In this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo is considered. We study a generalization of the Gerber–Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin; and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure, where the claim severities follow a combination of exponentials, is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.     

Recursions and fast Fourier transforms for a new bivariate aggregate claims model

Insurance companies typically face multiple sources (types) of claims. Therefore, modelling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In this paper, we first introduce a multivariate aggregate claims model, which allows dependencies among claim numbers as well as dependencies among claim sizes. For this proposed model, we derive recursive formulas for the joint probability functions of different types of claims. In addition, we extend the concept of exponential tilting to the multivariate fast Fourier transform and use it to compute the joint probability functions of the various types of claims. We provide numerical examples to compare the accuracy and efficiency of the two computation methods.     

About a duration index for life insurance contracts

Abstract

In this paper, after having defined the duration for a “generic” life insurance contract, we bring out some of its properties. We also prove that, in some cases, duration is a natural extension of well-known duration indices.     

On a conjecture related to the ruin probability for nonhomogeneous exponentially distributed claims

Recently, some recursive formulas have been obtained for the ruin probability evaluated at or before claim instants for a surplus process under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim revenues, which are assumed to be independent, identically distributed, following an arbitrary distribution. Based on numerical examples, a conjecture has also been stated relating the order in which the claims arrive to the magnitude of the corresponding ruin probability. In this paper, we prove this conjecture in the particular case when the claims are all exponentially distributed with different parameters.     

保险公司资产组合与最优投资比例研究

保险公司收益主要来源于承保利润和投资收益,其中承保利润受政策变动、市场条件等外部环境的影响较大,而投资收益则更多地取决于保险公司的投资能力,因此保险公司如何构建资产组合、如何确定最优投资比例就是获取投资收益最大化的重要因素。本文通过理论推导得出了保险公司的资产组合模型并运用非线性规划求解出最优投资比例,进而根据保险公司的投资数据进行了实证研究,为我国保险公司的资产组合及最优投资比例提供了一个可借鉴的思路。     

寿险公司内部控制问题探析

当今社会经济的日益繁荣及经济来往的多元化、复杂化,使寿险公司的经营面临着诸多风险,加强内部控制研究和实施就成为寿险公司亟待解决的一个问题。本文揭示了内部控制的涵义和本质,描述了寿险公司内部控制的特点和目前存在的问题,提出了加强寿险公司内部控制应采取的对策:强化内部控制在战略管理中的地位;寿险公司内部控制作为核心竞争力的培育;建立寿险公司内部控制标准;提升内部控制设计思路;加强内部控制的执行力等。     

The use of phase-type models for disability insurance calculations

This paper explores the use of phase-type models in actuarial calculations for disability insurance. We demonstrate that the changes in status of disability insureds can be appropriately captured by a phase-type model. Our model represents the aging process as the passage through a number of phases of decreasing vitality. When disabled, individuals additionally pass through several stages that represent duration of disability. Recovery and mortality rates from the earlier stages are greater than those in later stages. Using such a model, explicit and easily calculable expressions are obtained for relevant probabilities and actuarial present values. This facilitates the calculation of premiums and reserves.     

A rating model for loss of profits insurance

Abstract

In this paper we present a rating model for loss of profits insurance for a production system consisting of n production units. Explicit expressions for the company's long run expected average claims expenditures are derived. A numerical example is given.     

Separation of small and large claims on the basis of collective models

This paper is inspired by two papers of Riegel who proposed to consider the paid and incurred loss development of the individual claims and to use a filter in order to separate small and large claims and to construct loss development squares for the paid or incurred small or large claims and for the numbers of large claims. We show that such loss development squares can be constructed from collective models for the accident years. Moreover, under certain assumptions on these collective models, we show that a development pattern exists for each of these loss development squares, which implies that various methods of loss reserving can be used for prediction and that the chain ladder method is a natural method for the prediction of future numbers of large claims.     

On the accuracy of phase-type approximations of heavy-tailed risk models

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.     

Inequalities for the De Pril approximation to the distribution of the number of policies with claims

In the present paper, we give sufficient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given.     

A hierarchical model for the estimation of claim rates in a motor car insurance portfolio

Abstract

The present paper gives practical examples involving motor car insurance portfolios which we believe provide a natural setting in which collateral data should be used. In passing, the problem of assigning partial credibility is solved and an application of the empirical linearized Bayes estimators to experience rating is discussed.     

数据挖掘技术在寿险业交叉销售中的应用

一般来说,保险公司获得新客户的成本比维持老客户的成本要高得多,因此保险公司开始更多地关注现有客户的发展,交叉销售正是挖掘现有客户的消费潜力的有效方法。本文以CRISP-DM(Cross-Industry Standard Process for Data Mining)方法论为基础,探讨聚类分析和关联规则在寿险行业交叉销售中的应用,并结合某寿险公司的基础数据应用Clementine挖掘工具建立了交叉销售模型,帮助寿险公司有针对性地开展产品营销。     

The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims

We derive expressions for the density of the time to ruin given that ruin occurs in a Sparre Andersen model in which individual claim amounts are exponentially distributed and inter-arrival times are distributed as Erlang(n,?β). We provide numerical illustrations of finite time ruin probabilities, as well as illustrating features of the density functions.     

Integral and differential equations for the moments of multistate models in health insurance

The moments of the random future liabilities of health insurance policies are key quantities for studying distributional properties of the future liabilities. Assuming that the randomness of the future health status of individual policyholders can be described by a semi-Markovian multistate model, integral and differential equations are derived for moments of any order and for the moment generating function. Different representations are derived and discussed with a view to numerical solution methods.     

万能寿险内在收益率测算与影响因素分析

保单实际收益率的衡量指标,指出结算利率不能如实反映保单收益率。通过构造定期寿险和投资组合的方式,提出以万能寿险保单资金账户内在收益率IRR来反映实际收益率较为合适,文章以目前中国市场上正在销售的B款万能终身寿险产品为样本对保单IRR进行了测算,结果表明保单IRR低于结算利率,用结算利率来反映保单收益会对投保人产生误导,文章还进一步对万能寿险保单IRR的影响因素做了分析,结果表明保单持有时间长度、费用的比例和结构等因素显著影响保单收益。最后,文章根据测算和分析的结果给出了相应的建议。     

Analysis of a threshold dividend strategy for a MAP risk model

We consider a class of Markovian risk models in which the insurer collects premiums at rate c₁(c₂) whenever the surplus level is below (above) a constant threshold level b. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the LST (with respect to time) of the joint distribution of the time to ruin, the surplus prior to ruin, and the deficit at ruin. By interpreting that the insurer pays dividends continuously at rate c₁?c₂ whenever the surplus level is above b, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained by making use of an existing connection which links an insurer's surplus process to an embedded fluid flow process.