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。     

一类随机利率下的增额寿险模型

对寿险中的利率随机性问题的研究是近几年来保险精算研究的热点和重点问题之一。本文以即时给付的一类增额寿险为对象,考虑到突发事件对利率的影响,对随机利率采用Gauss过程与Poisson过程联合建模,给出即时给付的增额寿险的给付现值的各阶矩,并在一些特殊条件下给出矩的简洁表达式。     

随机利率下的增额寿险

我们考虑即时给付的增额寿险模型,根据保费的实际投资情况以及突发事件对利率的影响,将随机利率采用反射布朗运动(RBM)和Poisson过程联合建模,给出即时给付的增额寿险的给付现值的各阶矩,并在死亡均匀分布的条件下得到矩的简洁表达式．最后用数值例子说明模型与计算方法的正确性与有效性．     

随机利率寿险模型

本文针对随机利率寿险模型 ,考虑一保单组的平均给付额的性质 .通过对模型的结果分析 ,可以看出投保人数的增加 ,并未降低随机利率的风险 .本文针对一特殊的随机利率模型 ,给出了随机利率与常数利率的平均给付成本的比较     

一类随机利率下的变额寿险模型研究

本文对随机利率采用在原点反射的布朗运动以及负二项分布建模，具体以即时给付的综合人寿保险模型为研究对象，对寿险理论中的保费，年金以及责任准备金进行研究，并给出相应的表达式。     

随机利率下增额寿险现值函数矩的一些结果

本文对随机利率采用 Wiener过程和 Orentein- Uhlenbeck过程建模 ,得到了增额寿险现值函数的矩的一些结果     

随机利率下的增额寿险模型

以即时给付的增额寿险为研究对象,在保证利率恒正的情况下,考虑到不同性质的信息对利率的影响,对利率的随机性采用带Poisson跳的反射Brown运动建模,给出了一次缴清净保费、净均衡年保费和连续缴费方式下S时刻责任准备金的一般表达式.     

变额年金与变额寿险给付额的计算

目前在人寿保险中，如何对付通货膨胀的不良影响，使对被保人的实际保障不致降低是一个重要问题。变额年金与变额寿险是因应通货膨胀的寿险产品中最有效的，但其给付额的计算比较复杂。本文扰某些变额年金与交额寿险保单的给付额的确定做了推导，并分析了利差在克服通货膨胀影响中的作用。     

随机利率条件下最优投资消费与寿险购买策略

随着我国利率市场化的深入发展, 利率的随机波动对投资者的最优投资消费策略将产生重要影响. 与此同时, 随着我国寿险市场的渐趋完善, 寿险购买也越来越受到投资者的重视, 投资者的最优策略也将发生改变. 现研究由 Vasicek 模型来刻画的随机利率条件下最优投资消费与寿险购买策略. 投资者的目标在于选择最优投资消费与寿险购买策略使期望效用最大化. 通过运用 Legendre 转换方法求出最优投资消费与寿险购买的显性解. 通过数值分析的方法, 实证分析相关变量的变化对投资者最优投资与寿险购买策略的影响.     

多利率下的寿险费率测算模型

为了能够在多利率条件下测算人寿保险的费率,本文建立了一个线性规划模型.根据该模型,能够合理安排保费资金的投资期限以达到最大的保险利益,从而为费率和红利的测算提供了依据.列出了两个典型寿险产品的计算数据,结果表明,寿险费率的测算主要取决于长期利率.对于储蓄型寿险,资金的运用应该以长期投资为主,分红水平可以由长期利率与预定利率之差来确定.     

Analysis of survivorship life insurance portfolios with stochastic rates of return

A general portfolio of survivorship life insurance contracts is studied in a stochastic rate of return environment with a dependent mortality model. Two methods are used to derive the first two moments of the prospective loss random variable. The first one is based on the individual loss random variables while the second one studies annual stochastic cash flows. The distribution function of the present value of future losses at a given valuation time is derived. For illustrative purposes, an AR(1) process is used to model the stochastic rates of return, and the future lifetimes of a couple are assumed to follow a copula model. The effects of the mortality dependence, the portfolio size and the policy type, as well as the impact of investment strategies on the riskiness of portfolios of survivorship life insurance policies are analyzed by means of moments and probability distributions.     

多生命状态增额寿险的双随机模型

In this paper the dual random model of increasing life insurance for multiple-life status is discussed. The rnth moment of the present value of benefits are calculated and the respective expressions of the moments under joint life status or last- survivor status are presented.Fur-thermore,the limiting distribution of average cost of a portfolio of increasing life insurance for multiple-life status is studied.     

Optimal asset allocation for a general portfolio of life insurance policies

Asset liability matching remains an important topic in life insurance research. The objective of this paper is to find an optimal asset allocation for a general portfolio of life insurance policies. Using a multi-asset model to investigate the optimal asset allocation of life insurance reserves, this study obtains formulae for the first two moments of the accumulated asset value. These formulae enable the analysis of portfolio problems and a first approximation of optimal investment strategies. This research provides a new perspective for solving both single-period and multiperiod asset allocation problems in application to life insurance policies. The authors obtain an efficient frontier in the case of single-period method; for the multiperiod method, the optimal asset allocation strategies can differ considerably for different portfolio structures.     

Stochastic analysis of life insurance surplus

The aim of the paper is to examine the behavior of insurance surplus over time for a portfolio of homogeneous life policies. We distinguish between stochastic and accounting surpluses and derive their first two moments. A recursive formula is proposed for calculating the distribution function of the accounting surplus. We then examine the probability that the accounting surplus becomes negative in a given insurance year. Numerical examples illustrate the results for portfolios of temporary and endowment life policies assuming a conditional AR(1) process for the rates of return.     

随机利率下的保险精算函数

保险产品的定价离不开保险精算函数的运用 ,而保险精算函数的不确定性由剩余寿命和利率的不确定性决定 ,大数定律保证了通过大量出售保单可以减少死亡带来的风险 ,而要减少利率风险却非常困难 .本文讨论随机利率下的保险精算函数 ,分别求出这些精算函数的分布和矩 ,使我们对保险精算中的利率风险有更全面深入的认识 .     

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.     

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.     

Optimal investment and life insurance strategies under minimum and maximum constraints

We derive optimal strategies for an individual life insurance policyholder who can control the asset allocation as well as the sum insured (the amount to be paid out upon death) throughout the policy term. We first consider the problem in a pure form without constraints (except nonnegativity on the sum insured) and then in a more general form with minimum and/or maximum constraints on the sum insured. In both cases we also provide the optimal life insurance strategies in the case where risky-asset investments are not allowed (or not taken into consideration), as in basic life insurance mathematics. The optimal constrained strategies are somewhat more complex than the unconstrained ones, but the latter can serve to ease the understanding and implementation of the former.