Time-risk Discount Valuation of Life Contracts

In this paper a new approach is developed to value life insurance contracts by means of the method of backward stochastic differential equation. Such a valuation may relax certain market limitations. Following this approach, the values of single decrement policies are studied and Thiele‘s-type PDEs for general life insurance contracts are derived.     

递增年金的双随机模型

The dual random models about the life insurance and social pension insurance have received considerable attention in the recent articles on actuarial theory and applications. This paper discusses a general kind of increasing annuity based on its force of interest accumulationfunction as a general random process. The dual random model of the present value of the benefits of the increasing annuity has been set, and their moments have been calculated under certainconditions.     

Valuation of Life Insurance Products with Stochastic Interest Rates

IntroductionThe interest rate is an important factor affecting the value of life insurance productsbecause of their long period of time.As the interest rate is an undetermined variable,pricinglife insurance products under determined interest rates will ob…     

A NEW WAY TO ESTIMATE THE PARAMETERS IN THE PROGRESSIVE STRESS ACCELERATED LIFE TESTING

Among the three types of accelerated life testing, that is, the constant stress accelerated life testing, the step stress accelerated life testing, and the progressive stress accelerated life testing, the last one is the most effective and economical way to get the failure times of products in a short period of time. In this artiele a deficiency inthe classical approach is pointed out and a new method for the statisticul analysis of lifedata, especially for electronic products, under progressive stress (voltage) V(t)=Kt is given. Using the Bayesian method, for certain choices of the prior distribution, several forms of estimators of the parameters in the noraml stress We|bull distribution and the htverse power law model are derived. In particular, when the new shape parameter computers. The formulations are given for the general case and are illustrated for a special sitnpio case. comparison with the classical approach using pseudorandom dataas well as real data on solid tantatum electrolytic capacitors shows that the proposed method is better and more effective.     

Dynamic concept of returns to scales and its characteristics on production frontier in intersection form

This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale(RTS) of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit(DMU) with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs’ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.     

THE OPTIMAL DEDUCTIBLE AND COVERAGE IN INSURANCE CONTRACTS AND EQUILIBRIUM RISK SHARING POLICIES

In this paper, we consider the optimal risk sharing problem between two parties in the insurance business: the insurer and the insured. The risk is allocated between the insurer and the insured by setting a deductible and coverage in the insurance contract. We obtain the optimal deductible and coverage by considering the expected product of the two parties’ utilities of terminal wealth according to stochastic optimal control theory. An equilibrium policy is also derived for when there are both a...     

Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored Data

Length-biased data are encountered in many fields,including economics,engineering and epidemiological cohort studies.There are two main challenges in the analysis of such data:the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data.In this paper,a proportional mean residual life varyingcoefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model.Asymptotic properties are investigated for the proposed estimators.The finite sample performance of the proposed methodology is demonstrated by simulation studies.Finally,the method is applied to a real data set concerning the Academy Awards.     

有随机利率的多维风险模型有限时间破产概率

In this paper, assuming that there are s types of insurance contracts in an insurance company, we study the asymptotic of the finite-time ruin probability for the discrete-time multi-risk model.     

Markov-modulated mean-variance problem for an insurer

In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.     

Existence and Nonexistence of Global Classical Solutions to Porous Medium and Plasma Equations with Singular Sources

Let Ω be a bounded or unbounded domain in R^n. The initial-boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains.     

一种构造连生状态生命表的简单易行方法:方法和理论(英文)

在多生命模型中,几乎所有精算学教科书都假设被保险人的剩余寿命之间相互独立.本文中我们研究两生命模型.我们认为剩余寿命是正相依的,并用正象限相依描述相依性,给出了一种简单方法构造联合生命表.     

Applications of a multi-state risk factor/mortality model in life insurance

Mortality rates are known to depend on socio-economic and behavioral risk factors, and actuarial calculations for life insurance policies usually reflect this. It is typically assumed, however, that these risk factors are observed only at policy issue, and the impact of changes that occur later is not considered. In this paper, we present a discrete-time, multi-state model for risk factor changes and mortality. It allows one to more accurately describe mortality dynamics and quantify variability in mortality. This model is extended to reflect health status and then used to analyze the impact of selective lapsation of life insurance policies and to predict mortality under reentry term insurance.     

基于因子分析的中国寿险公司经营效率综合评价

利用财务指标法评价寿险公司绩效的一个重要特点就是主观赋权,而主观赋权一方面会导致对某个或某些因素过高或过低的估计,使评价结果不能如实反映寿险公司的真实情况,另一方面会诱使寿险公司粉饰或追求权重较高的指标.利用因子分析法,以2007年在我国境内开展业务的34家寿险公司作为样本,选择17个指标构建截面数据体系,对样本公司的风险水平和经营绩效进行评价.结果表明,老牌中资寿险公司保持着强大的综合实力,仍然是我中国人寿险市场的主导;外资寿险公司逐步加大规模扩张,资产管理能力不容轻视.     

一类随机利率下的增额寿险

寿险中的利率随机问题，是近来保险精算研究的热点和重点问题之一。本以即时给付的一类增额寿险为对象，对随机利率采用Gauss过程建模，研究给付现值及其各阶矩。     

Applications of a multi-state risk factor/mortality model in life insurance

Mortality rates are known to depend on socio-economic and behavioral risk factors, and actuarial calculations for life insurance policies usually reflect this. It is typically assumed, however, that these risk factors are observed only at policy issue, and the impact of changes that occur later is not considered. In this paper, we present a discrete-time, multi-state model for risk factor changes and mortality. It allows one to more accurately describe mortality dynamics and quantify variability in mortality. This model is extended to reflect health status and then used to analyze the impact of selective lapsation of life insurance policies and to predict mortality under reentry term insurance.     

随机利率下的增额寿险

寿险中的利率随机性问题，是近年来保险精算研完的热点之一，本文以即时给付的毒额寿险为对象，对随机利率采用Gauss过程建模，研究给付现值及其各阶矩，并在死亡均匀分布假设下得到矩的简洁表达式。     

A note on multiple life premiums for dependent lifetimes

We study the properties of multiple life annuity and insurance premiums for general symmetric and survival statuses in the case when the joint distribution of future lifetimes has a dependence structure belonging to some nonparametric neighbourhood of independence. The size of the neighbourhood is controlled by a single parameter, which enables us to model really weak as well as stronger dependencies. We provide bounds on the difference of multiple life premiums for vectors of dependent and independent future lifetimes with the same univariate marginal distributions. Each such upper bound can be treated as a premium loading related to the strength of lifetimes’ dependence.     

随机利率下的增额寿险模型研究

在实际的保险精算中,保单保险金现值函数的期望就是该种保单的纯保费,而方差常用来度量该种保单的风险.对随机利率采用W iener过程建模,得到了增额寿险保险金现值函数的期望和方差.     

Life insurance in a portfolio context

The ownership of life insurance may be modeled as a portfolio problem in which the return on the life insurance contract is negatively correlated with the return on a claim to future wage income. The mean-variance model developed in the paper uses such a framework to express the optimal amount of insurance in terms of two components: the expected value of the wage claim and the risk/return characteristics of the insurance contract. The model thus offers an appealing way to formulate the life insurance problem in a portfolio context. Implications of the model for the functioning of a life insurance market are examined and the existence of accidental death contracts is explained.