某些保险风险序的性质及其相互关系

本文讨论了几种保险风险次序的性质及它们之间的相互关系 ,利用停止损失限额变换的特性讨论了停止损失收敛的性质和在极限状态下风险次序的传递闭包的性质 ,得到了停止损失收敛的一种等价表示 ,并对两种具体风险序的传递闭包给出了等价的风险序表示 .     

保险公司和再保险公司之间的停止损失再保险策略选择博弈

本文在扩散逼近风险模型下考虑保险公司和再保险公司之间的停止损失再保险策略选择博弈问题.假设保险公司和再保险公司都以期望终端盈余效用增加作为购买停止损失再保险和接受承保的条件.在保险公司和再保险公司都具有指数效用函数条件下,运用动态规划原理,通过求解其对应的Hamilton-Jacobi-Bellman方程,得到了三种博弈情形下保险公司和再保险公司之间的停止损失再保险策略和值函数的显示解,以及再保险合约能够成交时再保费满足的条件.结果显示,在适当的条件下,保险公司和再保险公司之间的停止再保险合约是可以成交的.最后,通过灵敏性分析给出了最优停止损失再保险策略和再保费,以及效用损益与模型主要参数之间的关系,并给出相应的经济分析.     

个体风险模型的Poisson复合模型近似

本文在近乎最一般的假定下，简述了个体风险模型的Poisson复合模型近似．特别地，借助风险间停止损失保费的总差异给出了这一近似的精度．     

关于停止损失再保险的调节系数最大化问题

停止损失再保险作为一种再保险方式,在具有相同保费的前提下,能使保险人的期望效用最大,并能使其自留风险方差最小.另外在保费和费率相等的前提下,停止损失再保险的调节系数不可能比其他再保险方式的调节系数小.本论文在此基础上作了相应推广,讨论了在保费相等的前提下,停止损失再保险的费率满足时,其调节系数不小于其他再保险方式的调节系数.     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本研究了离散型随机变量次序统计量的分布矩阵的对称性,获得了二个定理。定理1服从等概率二点分布等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵。定理2取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性。     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1　服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2　取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .     

停止变换的不变性

利用条件期望的表达式给出了两指标过程在停线处的停止定义,研究了停止变换下的若干不变性．给出了这种停止意义下的局部平方可积强鞅的定义,进一步研究了局部平方可积强鞅二次变差的存在性及其停止性质，得到了重要的Burkholder-Davis-Gundy型不等式及平方可积强鞅的一个充要条件。     

保险风险模型的序关系及其误差

从停止损失序的角度,探讨了用集体风险模型来近似个体风险模型时,随机风险理赔总额S的一般情况,我们推广现有文献(如Goovaerfs)的关于单因模型的结果,得到了各模型间S的序的关系(定理1),并给出了各模型S之间的误差公式(定理3).     

关于次序统计量广义TTT序的几个结果

研究了次序统计量在广义TTT变换序(TTT变换序)和剩余财富序下的性质. 讨论了寿命分布类NBUT在增凹变换下的封闭性以及NWUT寿命分布在次序统计量下的特征.     

模糊Fourier变换算法

本文把普通集合中的离散Fourier变换推广到模糊集合。借助于区间数、模糊数的运算规则及有关性质,给出了模糊离散Fourier变换(FDFT)的定义及算法,而且也讨论了模糊离散Fourier变换中的对应关系以及变换性质的几个定理。     

离散随机序在复合二项破产模型中的应用

本文的内容由三部分组成 .首先 ,在简述复合二项破产模型近期已得的相关成果的基础上 ,给出了最终破产概率的复合几何分布表示 ;接着 ,在概述了离散随机优序与停止损失序的主要结果后 ,首次提出了幂序的概念 ;最后 ,借助上述离散随机序 ,在复合二项破产模型中探讨了个体索赔额对于最终破产概率与调节系数的影响     

个体风险模型的Poisson复合模型近似

本文首先简要介绍了停止损失序在风险期望值相等时的一些推论 ,然后借助停止损失序详尽地讨论了仅取有限个值的随机变量的格点化 ,并以此作为出发点在多重衰减模型的框架下 ,给出了以 Poisson复合模型近似个体风险模型的一般步骤 ,同时导出了评价这一近似优劣程度的一个数量指标的解析表达式。     

Extension of a quadratic transformation due to Exton

By applying various known summation theorems to a general formula based upon Bailey’s transform theorem due to Slater, Exton has obtained numerous new quadratic transformations involving hypergeometric functions of two and of higher order. Some of the results have typographical errors and have been corrected recently by Choi and Rathie. In addition, two new quadratic transformation formulæ were also obtained [Junesang Choi, A.K. Rathie, Quadratic transformations involving hypergeometric functions of two and higher order, EAMJ, East Asian Math. J. 22 (2006) 71-77]. The aim of this research paper is to obtain a generalization of one of the Exton’s quadratic transformation. The results are derived with the help of generalized Kummer’s theorem obtained earlier by Lavoie, Grondin and Rathie. As special cases, we mention six interesting results closely related to that of Exton’s result.     

On prices' evolutions based on geometric telegrapher's process

The geometric telegrapher's process is proposed as a model to describe the dynamics of the price of risky assets. When the underlying random inter‐times have Erlang distribution we express the probability law of such process in terms of a suitable two‐index pseudo‐Bessel function. Stochastic comparisons of two geometric telegrapher's processes based on the usual stochastic order (FSD comparison) and on the stop‐loss order are also performed. Various examples of application of such comparisons are then provided. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal control policy for a standing order inventory system

In this paper, we consider a standing order inventory system in which an order of fixed size arrives in each period. Since demand is stochastic, such a system must allow for procurement of extra units in the case of an emergency and sell-offs of excess inventory. Assuming the average-cost criterion, Rosenshine and Obee (Operations Research 24 (1976) 1143–1155) first studied such a system and devised a 4-parameter inventory control policy that is not generally optimal. The current paper uses dynamic programming to determine the optimal control policy for a standing order system, which consists of only two operational parameters: the dispose-down-to level and order-up-to level. Either the average-cost or discounted-cost criterion can be assumed in the proposed model. Also, both the backlogged and lost-sales problems are investigated in this paper. By using a convergence theorem, we stop the dynamic programming computation and obtain the two optimal parameters.     

Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhorn's Version of Wigner's Theorem

We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.     

Controllability of nonlinear fractional order integrodifferential system with input delay

This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results.     

多目标条件风险值问题的等价定理

条件风险值问题是研究信用风险最优化的一种新的模型，本文研究了一类多目标条件风险值问题等价定理，我们引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值(最小信用风险值)和α-CVaR损失值(最小信用风险值对应的条件期望损失值或条件风险价值度量)概念，为了求得α-CVaR损失值下的弱：Pareto有效解，我们证明了它等价于求解另一个多目标规划问题的Pateto有效解，这样使得问题的求解变得简单．     

Probabilistic mean value theorems for conditioned random variables with applications

In this paper, we propose a probabilistic analogue of the mean value theorem for conditional nonnegative random variables ordered in the hazard rate and reversed hazard rate order, upon conditioning on intervals of the form (t,∞) and [0,t]. This result is then specialized within the proportional hazards model and the proportional reversed hazards model with applications to series systems in reliability theory and to absorption random times of linear birth‐death processes. We also study the comparison of residual entropies and discuss some connections to Wasserstein and stop‐loss distances of random variables. A treatment for the additive hazard rate model is finally provided, with an application to life annuities.     

Comonotonic convex upper bound and majorization

When the dependence structure among several risks is unknown, it is common in the actuarial literature to study the worst dependence structure that gives rise to the riskiest aggregate loss. A central result is that the aggregate loss is the riskiest with respect to convex order when the underlying risks are comonotonic. Many proofs were given before. The objective of this article is to present a new proof using the notions of decreasing rearrangement and the majorization theorem, and give clear explanation of the relation between convex order, the theory of majorization and comonotonicity.