从精算的角度看保险组合的定价

就目前的保险市场来看,保险产品几乎包括了各种类别,不论是传统的寿险产品还是新型分红和投连产品,提供的保障基本上满足了市场的不同需求。与     

我国健康保险精算方法研究现状分析

本文首先对健康保险精算的具体内容进行了探讨,进而概括了我国健康保险的四类精算方法:粗估法、模型法、基于保险损失分布模型的测算方法、经验频数法和限制性Pareto分布法,并且对这几种方法的局限性作了一定的分析。     

随机利率对人寿保险产品定价的影响研究

本文以全离散式的寿险模型为研究对象,借助于敏感性分析技术和Monte-Carlo模拟技术分析了各种利率参数对于一次趸缴和年均衡支付保费的生存险和死亡保险商品价格的影响,并确定一次趸缴和年均衡支付保费的生存险和死亡保险产品的价格。     

基于固定利率的精算模型研究

随着社会和经济的发展,我国医疗水平和人们生活水平不断提高,人们的平均寿命延长,老年人口占总人口的比例日益攀升,人们对养老保障的关注度和要求也越来越高。目前,对养老保险的研究多局限于制度方面的定性分析,而忽略了从精算学角度出发的定量分析,本文就我国社会养老保险为研究资料,根据相关制度以及精算学中利息理论等相关理论知识对基于固定利率的精算模型进行了分析和研究,发现其中的问题并进行了优化和改善。     

《易经》的精算回望与保险精算的易理

通过对《易经》的回望,现代保险精算可以从中找到“安身立命”之道。本文分别从三个方面阐述了两者之间的内在逻辑。首先,保险精算的本质内涵是由“易”求“定”的过程;其次,“占”也是现代保险精算的重要功能之一;再次,保险精算通过“数”的归因分析,去探索并构建“模型”,“模型”是为了解释和理解现象,并借此判断趋势和预测未来。保险精算要从“义理”与“象数”的关系中认识到,“象数”的最终目的不仅是追求“真理”,更要追求“义理”,这是保险精算的真谛,也是保险精算的价值所在。     

不同借贷利率下的欧式外汇期权定价的保险精算方法

本文在假定借贷利率大于或等于债券利率,股票的期望收益率、波动率和红利率都随时间变化的情况下,利用保险精算法给出欧式看涨和看跌期权的定价公式.同时根据借贷利率对期权价格的影响,得到欧式看涨和看跌期权价格的显示解,以及两者之间的平价关系.进一步把结论推广扩展到欧式外汇期权的定价关系,并进行相应的灵敏度分析     

保险精算学原理在可转债定价模型中的运用

可转债作为一种新型金融衍生工具,其价值可以简单理解为转股权价值与债券价值之和。MogensBladt与Tina Hvid Rydberg于1998年首先提出期权定价的保险精算方法,但是其结果与Black—scholes公式存在一定出入,在修正Bladt和Rydberg提出的精算公式基础上,从评估实际损失和相应概率分布角度来定量研究可转债期权部分价值,获得基于保险精算方法的可转债期权部分定价模型。同时,基于精算等价原理,通过每一违约事件在某时刻发生概率和该时刻债券支付现金流,得到债券未来支付现金流的精算现值,即可转债债券部分的精算价格。通过两部分价值模型的建立,得到可转债的定价模型。精算方法在一定程度克服了基于无风险套利、复制思想得到的B-S模型假设严格、公式推导较为繁琐的不足,同时,可转债债券部分的风险也能够通过精算方法得到较好体现。     

巨灾指数选择权模型及定价方法

考虑短期随机利率下,损失指数价值过程为带复合Poisson跳过程的几何Brown运动模型时巨灾指数选择权的定价问题,用保险精算方法得到了选择权的精确定价解和买权卖权间的平价关系,和传统无套利方法下巨灾指数选择权的定价进行了比较,并推广了保险精算定价法相关结果。     

随机利率理论下的定期寿险

近年来关于随机性问题的研究成为了精算界的热点之一,本文将针对寿险精算当中的随机利率进行讨论,建立一种随机利率ARCH时间序列模型,对随机利率下的定期寿险同题进行了进一步的理论探讨和实证研究.     

Recursive Moments of Compound Renewal Sums with Discounted Claims

Under regularity conditions, Le´veille´& Garrido [6] gives a derivation of the first two moments (resp. asymptotic) of a Compound Renewal Present Value Risk (CRPVR) process using renewal theory arguments. In this paper, with the same procedure and assuming that all the moments of the claim severity and the claims number process exist, we get recursive formulas for all the moments (resp. asymptotic) of the CRPVR process.     

基于分数维随机利率的分数跳-扩散外汇期权定价

假设利率为分数维随机利率,外汇汇率服从分数跳一扩散过程,并且波动率为常数,期望收益率为时间的非随机函数,本文利用保险精算方法,得出了看涨、看跌外汇欧武期权的一般定价公式,并建立了平价公式。     

新农保个人账户设计的改进：基于精算模型的分析

根据国务院《关于开展新型农村社会养老保险试点的指导意见》,对新农保个人账户的精算结果表明：（1）采取固定额度缴费,个人账户积累基金将会累退式增长,且在缴费超过30年后,会出现缴费时间越长,替代率越低的现象;（2）大龄参保农民如果选择较低档次缴费,个人账户养老金基本起不到保障作用;（3）政府对个人账户的缴费补贴机制,不足以激励参保农民在经济条件许可的情况下,选择较高档次参保。基于此,应以固定费率取代固定额度缴费;建立缴费补贴的激励机制,引导大龄参保农民选择较高档次缴费;给予个人账户基金合理的计息利率;建立弹性领取养老金年龄机制。本文均通过精算模型对上述改进建议进行了模拟测算。     

Insurance Considering a New Stochastic Model for the Discount Factor

In many empirical situations (e.g.: Libor), the rate of interest will remain fixed at a certain level (random instantaneous rate i i ) for a random period of time ( t i ) until a new random rate should be considered, i i + 1 , that will remain for t i + 1 , waiting time until the next change in the rate of interest. Three models were developed using the approach cited above for random rate of interest and random waiting times between changes in the rate of interest. Using easy integral transforms (Laplace & Fourier) we will be able to calculate the moments of the probability function of the discount factor, V ( t ), and even its c.d.f. The approach will also be extended to the calculation of the expected value (net premium) and variance of a term insurance and we will get its c.d.f., something not very common in actuarial literature due to its complexity, but very useful when the law of large numbers cannot be applied and consequently use normal approximations.     

Analysis of ruin measures for the classical compound Poisson risk model with dependence

In this paper, we consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie–Gumbel–Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber–Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution.     

A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback

Recent market events have reinvigorated the search for realistic return models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market with both fundamental and technical traders. This is based on a trade arrival model with variable size orders and a general arrival-time distribution. With simplifications we are led in the jump-free case to a local volatility model defined by a hybrid SDE mixing both arithmetic and geometric or CIR Brownian motions, whose solution in the geometric case is given by a class of integrals of exponentials of one Brownian motion against another, in forms considered by Yor and collaborators. The reduction of the hybrid SDE to a single Brownian motion leads to an SDE of the form considered by Nagahara, which is a type of ‘Pearson diffusion’, or, equivalently, a hyperbolic OU SDE. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive naturally at an equilibrium fat-tailed return distribution with a Student or Pearson Type~IV form. Under less-restrictive assumptions, richer dynamics are possible, including time-dependent Johnson-SU distributions and bimodal structures. The phenomenon of variance explosion is identified that gives rise to much larger price movements that might have a priori been expected, so that ‘25σ’ events are significantly more probable. We exhibit simple example solutions of the Fokker–Planck equation that shows how such variance explosion can hide beneath a standard Gaussian facade. These are elementary members of an extended class of distributions with a rich and varied structure, capable of describing a wide range of market behaviors. Several approaches to the density function are possible, and an example of the computation of a hyperbolic VaR is given. The model also suggests generalizations of the Bougerol identity. We touch briefly on the extent to which such a model is consistent with the dynamics of a ‘flash-crash’ event, and briefly explore the statistical evidence for our model.