Tobit模型与税收稽查

一、Ｔｏｂｉｔ模型　　Ｔｏｂｉｔ模型是经济学家、1981年诺贝尔经济学奖获得者Ｊ·托宾(Ｊａｍｅｓ.Ｔｏｂｉｎ)1958年在研究耐用消费品需求时首先提出来的一个经济计量学模型。其基本结构如下:设某一耐用消费品支出为ｙｉ(被解释变量),解释变量为Ｘｉ,则耐用消费品支出ｙｉ要么大于ｙ0(ｙ0表示该耐用消费品的最低支出水平),要么等于零。因此,在线性模型假设下,耐用消费品支出ｙｉ和解释变量Ｘｉ之间的关系为:ｙｉ=βＴＸｉ ｅｉ若βＴＸｉ ｅｉ>ｙ00其他(1)ｅｉ～Ｎ(0,σ2),ｉ=1,2,…,ｎ其中,Ｘｉ是(ｋ 1)维的解释变量向量,β是(ｋ 1)维…     

关于期望寿命的估计

一、引言期望寿命又叫平均剩余寿命。设寿命 (或生存时间 )为Ｘ ,则在Ｘ >ｔ的条件下Ｘ -ｔ的期望ｅ =Ｅ(Ｘ -ｔ|Ｘ >ｔ)是期望寿命。设Ｘ的分布函数Ｆ(ｘ)是未知的 ,如何估计ｅｔ,这是保险精算、可靠性工程及生存分析等实际工作中很关心的问题。随机考察ｎ个个体 ,这些个体的寿命分别是ｘ1 ,ｘ2 ,… ,ｘｎ,他们被看作随机变量 ,相互独立 ,有相同的分布函数Ｆ(ｘ)。我们分别在一列时刻ａ0 =0 <ａ1<ａ2 <… <ａｍ 观测其寿命。令ａｍ + 1 =∞ ,Ｉｋ=(ａｋ,ａｋ + 1 ](ｋ =0 ,1,2 ,… ,ｍ)。考虑等距分组 ,即每个区间的长度都为ｈ ,ｈ =ａｋ +…     

不同分布状态下的个体风险模型的比较

一、问题的提出在保险精算学中,个体风险模型被用来计算同一险种的所有保单的索赔额。对某一险种的N个同质的保单,记其未来的索赔量分别为非负独立的随机变量狖Xk,k=1,2,…狚。设它们具有共同的分布函数F,则总的索赔量为Sx=Nk=1∑Xk。在保险风险理论中,称Sx为个体风险模型(Indi     

中国汽车保险奖惩系统的严厉性比较

在汽车保险中,大多数国家的保险人都使用了奖惩系统(BMS:Bonus MalusSystem),即根据被保险人在上一保险年度的索赔经验调整其次年的续期保费。奖惩系统也被称为无赔款折扣(NoClaimDiscount)系统。在BMS中,如果被保险人在过去的一个保险年度没有发生索赔,保险人将降低其续期保费,否则将提高其续期保费。这种调整只考虑被保险人是否发生索赔以及索赔次数的多少,而不考虑赔付金额的大小。迄今为止我国汽车保险业务中出现的奖惩系统,绝大多数属于这一类。在我国车险业务经营的20多年里,奖惩系统功不可没,根据形势和体制的变化,其内容进行了…     

浅议CS管理

ＣＳ是英文ＣｕｓｔｏｍｅｒＳａｔｉｓｆａｃｔｉｏｎ的缩写 ,意为顾客满意。企业的整个经营活动要以顾客的观点满意为指针 ,要从顾客的角度、用顾客的观点而非自身的观点来分析、考虑消费者的需求。其基本观点和方法是 :把顾客需求 (包括潜在的需求 )作为企业开发产品的源头     

浅谈季节调整的方法及其应用

早在５０年代初，西方国家在统计 领域就开展了对季节调整方法的研究和应用。美国人口普查局在５０年代的人口统计中率先研制并应用了季节调整方法Ｘ－１，此种方法经过近几十年的不断实践、完善，逐步发展为Ｘ－１１ ＡＲＩＭＡ和Ｘ－１２ｒｅｇＡＲＩＭＡ，并为西方各大工业国广泛应用。在我国，由于数理统计基础相对薄弱，统计界对季节调整方法应用的系统研究起步较晚。在１９９３年国家统计局组织Ｂｕｓｉｎｅｓｓ ＣｙｃｌｅＡｎａｌｙｓｉｓ＆Ｆｏｒｅｃａｓｔ）—经济周期波动分析软件（ＢＣＡＭ）操作培训时，我国政府系统的统计工…     

经济循环帐户讲座(之十五)保险核算

经济循环帐户讲座（之十五）保险核算□许宪春一、１９９３年ＳＮＡ的保险核算（一）保险服务产出的计算保险公司通过收取保险费、支付保险索赔和保险金的方式提供保险服务，但它所收取的保险费并不就是保险服务费，因为保险费中的大部分是保险公司支付保险索赔和保险金的...     

中国经济增长的均衡路径分析

一、引言无论是新古典经济增长理论 ,还是新近兴起的内生经济增长理论 ,都认为每个经济都各自有一个均衡增长路径 ,并且都将收敛于其自身的这一稳态路径 ;一个经济离其均衡增长路径越远 ,收敛的速度就越快。经济增长的这一条件收敛性质 ,近年来已引起了不少西方著名经济学家的兴趣和关注 ,曼昆 (Ｎ .ＧｒｅｇｏｒｙＭａｎｋｉｗ)、罗默 (ＤａｖｉｄＲｏｍｅｒ)和韦尔 (ＤａｖｉｄＮ .Ｗｅｉｌ) ( 1 992 )曾用世界 98个国家和地区的截面数据对此条件收敛性质进行了实证研究 ,巴罗 (ＲｏｂｅｒｔＪ.Ｂａｒｒｏ)和萨拉伊马丁(ＸａｖｉｅｒＳａ…     

几种不同形式的标准正态统计数表的区别和联系

一、标准正态分布函数表(标准正态分布面积表)标准正态分布函数Ｆ(Ｘ)是反映随机变量Ｘ在某一区间内取值时相应的概率取值的一种函数。用公式表示为Ｆ(Ｘ)＝Ｐ(Ｘ＜Ｘ)＝∫－∞ｆ(Ｘ)ｄｘ,Ｘ∈(－∞,∞),标准正态分布函数表格及图示如下:     

广义Erlang模型下利率波动对保险资产的影响

0引言在研究保险资产的盈亏状态时,如果不考虑利率因素,那么最为基本的模型是风险理论中的Cramer-Lundberg模型。在该模型中,盈余过程的表达式为U(t)=u ct-N(t)i=1!Xi,这里u>0为保险公司的初始资本金,c>0为保率,N(t)为时刻t之前来到的索赔个数,索赔来到的过程服从泊松过程(即来     

Pólya–Aeppli of Order k Risk Model

In this study, we define the Pólya–Aeppli process of order k as a compound Poisson process with truncated geometric compounding distribution with success probability 1 ? ρ > 0 and investigate some of its basic properties. Using simulation, we provide a comparison between the sample paths of the Pólya–Aeppli process of order k and the Poisson process. Also, we consider a risk model in which the claim counting process {N(t)} is a Pólya-Aeppli process of order k, and call it a Pólya—Aeppli of order k risk model. For the Pólya–Aeppli of order k risk model, we derive the ruin probability and the distribution of the deficit at the time of ruin. We discuss in detail the particular case of exponentially distributed claims and provide simulation results for more general cases.     

The uniform local asymptotics for a Lévy process and its overshoot and undershoot

ABSTRACT

In this article, we obtain the uniform local asymptotics for a Lévy process with a heavy-tailed Lévy measure and for the overshoot and undershoot of the Lévy process. As applications, we get the uniform asymptotics of the finite-time ruin probability and the local ruin probability for the Lévy risk model with a heavy-tailed Lévy measure. By the above results, we find that in the compound Poisson model perturbed by a Brownian motion, the effect of the Brownian component on the asymptotics of the finite-time ruin probability and the local ruin probability washes out.     

The finite-time ruin probability of a discrete-time risk model with GARCH discounted factors and dependent risks

The finite-time ruin probability of a discrete-time risk model with dependent stochastic discount factors and dependent insurance and financial risks is investigated in this paper. Assume that the stochastic discount factors follow a GARCH process and the one-period insurance and financial risks form a sequence of independent and identically distributed random pairs, which are the copies of a random pair with a bivariate Sarmanov dependent distribution. When the common distribution of claim-sizes is heavy-tailed, we establish an asymptotic estimate for the finite-time ruin probability. Applying the result to a special case, we also get conservative asymptotic bounds. A numerical simulation is given at the end of the paper.     

A delayed dual risk model

In this article, we study a dual risk model with delays in the spirit of Dassios–Zhao. When a new innovation occurs, there is a delay before the innovation turns into a profit. We obtain large initial surplus asymptotics for the ruin probability and ruin time distributions. For some special cases, we get closed-form formulas. Numerical illustrations will also be provided.     

The severity of ruin in a discrete semi-Markov risk model

In this paper we introduce a discrete time semi-Markov risk model. We derive a recursive system for finding the probability of ruin and the distribution of the severity of ruin in a particular case where the annual result may be positive only in years beginning in some given state.     

On a discrete interaction risk model with delayed claims and stochastic incomes under random discount rates

In this paper, we study a discrete interaction risk model with delayed claims and stochastic incomes in the framework of the compound binomial model. A generalized Gerber-Shiu discounted penalty function is proposed to analyse this risk model in which the interest rates follow a Markov chain with finite state space. We derive an explicit expression for the generating function of this Gerber-Shiu discounted penalty function. Furthermore, we derive a recursive formula and a defective renewal equation for the original Gerber-Shiu discounted penalty function. As an application, the joint distributions of the surplus one period prior to ruin and the deficit at ruin, as well as the probabilities of ruin are obtained. Finally, some numerical illustrations from a specific example are also given.     

Gambler’s Ruin: The Duration of Play

We study the gambler’s ruin problem with a general distribution of the payoffs in each game. Assuming the expected value of the payoff distribution is negative, so that eventual ruin occurs with probability 1, we are interested in the distribution of the duration to ruin, also known as the first-passage time distribution. A generating function for this distribution is obtained. Exact expressions for the expected value and variance of this distribution, as well as asymptotic expressions for the case of large initial wealth, are derived.     

Upper bounds for ruin probabilities under model uncertainty

Abstract

In this paper, we investigate some ruin problems for risk models that contain uncertainties on both claim frequency and claim size distribution. The problems naturally lead to the evaluation of ruin probabilities under the so-called G-expectation framework. We assume that the risk process is described as a class of G-compound Poisson process, a special case of the G-Lévy process. By using the exponential martingale approach, we obtain the upper bounds for the two-sided ruin probability as well as the ruin probability involving investment. Furthermore, we derive the optimal investment strategy under the criterion of minimizing this upper bound. Finally, we conclude that the upper bound in the case with investment is less than or equal to the case without investment.     

The Ruin Probability of a Discrete-Time Risk Model with a One-Sided Linear Claim Process

In this article, the ruin probability is examined in a discrete time risk model with a constant interest rate, in which the dependent claims are assumed to have a one-sided linear structure. An explicit asymptotic formula is obtained for the ruin probability. Generalized Lundberg inequalities for the ruin probability are derived by martingale and inductive approaches.     

Estimate for the Finite-time Ruin Probability in the Discrete-time Risk Model with Insurance and Financial Risks

In this article, we consider a discrete-time risk model with insurance and financial risks. We derive some refinements of a general asymptotic formula for the finite-time ruin probability under the assumptions that the net losses follow a common distribution in the intersection between the subexponential class and the Gumbel maximum domain of attraction, and the stochastic discount factors of the risky asset have a common distribution with extended regular variation. The obtained asymptotic upper and lower bounds are transparent and computable.