指数保费原理下的经验厘定

在经典的信度理论中,信度保费是在净保费原理下得到的. 但是, 保险商业中, 保险公司要求制定的保费必须适用于某合适的保费原理以适应具体的保险商业的需要. 本文建立了指数保费原理下的完全经验厘定模型, 得到了风险保费的信度估计和经验Bayes 信度估计, 并讨论了结构参数的估计及其性质. 最后证明了多合同模型的经验Bayes 信度估计的渐近最优性     

On the consistency of credibility premiums regarding Esscher principle

In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions.     

The credibility premiums for models with dependence induced by common effects

In classical Bühlmann credibility models, claims are assumed to be independent between different risks. In many practical situations, however, this assumption may be violated because there are situations that could drive possible relationship among the insured individuals. This paper aims to extend the Bühlmann and Bühlmann-Straub credibility models to account for a special type of dependence between risks induced by common stochastic effects. By means of the projection method, the corresponding credibility premiums are obtained, which generalize some well known existing results in credibility theory.     

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Variance related premium principle is one of the most important principles not only in practice applications but also in research field of actuarial science. In this paper, the Bayesian models are established under variance related premium principle. The Bayesian estimate and credibility estimate of risk premium are derived. Furthermore, some statistical properties of estimators are discussed. In the models with multitude contract data, the unbiased consistent estimates of the structure parameters are proposed. Finally, the empirical Bayes estimator are proved to be asymptotically optimal.     

熵损失函数下的信度模型

本文研究了信度模型问题.利用熵损失函数,获得了风险保费的信度估计和经验Bayes信度估计.所获结果是对现有风险保费信度估计和经验Bayes信度估计的一个补充.     

Optimal risk and dividend control of an insurance company with exponential premium principle and liquidation value

Assume that an insurer can control it’s surplus by paying dividends, purchasing reinsurance and injecting capital. The exponential premium principle is used when pricing insurance contract instead of the expected value principle. Under the objective of maximizing the company’s value, we identify the optimal strategies with liquidation value and transaction costs. The results illustrate that the insurer should buy less reinsurance when the surplus increases, capital injection should be considered if and only if the transaction costs and the liquidation value are relatively low, dividends are paid according to barrier strategy if the dividend rate is unrestricted or threshold strategy if the dividend rate is bounded.     

Evaluating the lifetime performance index for the exponential lifetime products

Process capability indices (PCIs) are used to measure process potential and performance. Since the lifetime of products generally may possess an exponential, gamma or Weibull distribution, etc., so under a two-parameter exponential distribution, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the right type II censored sample. Then the UMVUE of the lifetime performance index is utilized to develop the new hypothesis testing procedure in the condition of known L. Finally, a practical example is illustrated to employ the testing procedure to determine whether the process is capable.     

A premium principle based on the g-integral

A novel approach of calculating an insurance premium based on g-integrals and interval-valued integrals is introduced. The characterization theorem for the g-integral-based premium principle is proven, and the relations with some well-known premium principles are discussed. The main properties of the interval-valued premium principle based on the g-integral are presented and some illustrative examples are given.     

Minimum divergence estimators,maximum likelihood and exponential families

The dual representation formula of the divergence between two distributions in a parametric model is presented. Resulting estimators do not make use of any grouping or smoothing. For smooth divergences they all coincide with the MLE on any regular exponential family.     

具有多合同的广义加权保费的信度估计(英文)

本文讨论了广义加权保费原理下的信度估计,并把结论推广到多合同模型.通过概率分布的变换,本文得到了多合同模型下广义加权保费的非齐次和齐次信度估计.并且讨论了这些估计的统计性质.最后,运用重抽样方法讨论了信度因子中未知结构参数的估计.数值模拟表明,非齐次信度估计能运用于保险实际.     

Pitman closeness results for Type-I censored data from exponential distribution

Recent work on Pitman closeness has compared estimators under Type-II censored samples from exponential distribution based on observed number of failures. In this paper, we carry out similar Pitman closeness comparisons for Type-I censored samples from exponential distribution based on time under test.     

指数保费准则下的最优投资和比例再保险

该文研究了保险公司的最优投资和比例再保险问题,其中假定保险公司的盈余过程为一个带扩散扰动的经典风险过程.假定再保险的保费按照指数保费原理来计算,这使得所研究的随机控制问题成为非线性的.该文同时考虑了最大化终端财富指数效用和最大化调节系数两类问题,并给出了最优值函数和相应的最优策略的解析表达.此外,该文还分析了再保险公司的风险厌恶和保险公司的不确定性参数对最优策略的影响.     

Balanced credibility estimation

This paper shows how a multivariate credibility estimator should be adjusted to satisfy a linear balancing constraint.     

An improved Mordell type bound for exponential sums

For a sparse polynomial , with and , we show that

thus improving upon a bound of Mordell. Analogous results are obtained for Laurent polynomials and for mixed exponential sums.

     

生存分析中乘积限估计的大样本性质

生存分析中，人们关心的问题之一是利用不完全的寿命调查数据估计生物折寿命分布。在实际问题中，比较常见的不完全数据包括右删失数据，左截断数据和左截断右删失数据。利用这三种数据估计寿命分布时，常用的统计量是乘积限估计。于是，乘积限估计的大样本性质的研究一直受到关注。本文就这方面的研究近况做一比较系统的论述。     

Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction

We present an accurate investigation of the algebraic conditions that the symbols of a non-singular, univariate, binary, non-stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials. A subdivision scheme is said to possess the property of reproducing exponential polynomials if, for any initial data uniformly sampled from some exponential polynomial function, the scheme yields the same function in the limit. The importance of this property is due to the fact that several curves obtained by combinations of exponential polynomials (such as conic sections, spirals or special trigonometric and hyperbolic functions) are considered of interest in geometric modeling. Since the space of exponential polynomials trivially includes standard polynomials, this work extends the theory on polynomial reproduction to the non-stationary context. A significant application of the derived algebraic conditions on the subdivision symbols is the construction of new non-stationary subdivision schemes with specific reproduction properties.     

On upper bounds of Chalk and Hua for exponential sums

Let be a polynomial of degree with integer coefficients, any prime, any positive integer and the exponential sum . We establish that if is nonconstant when read , then . Let , let be a zero of the congruence of multiplicity and let be the sum with restricted to values congruent to . We obtain for odd, and . If, in addition, , then we obtain the sharp upper bound .