解不适定算子方程的一个定常二步隐式迭代法

On the basis of an implicit iterative method for ill-posed operator equations,we introduce a relaxation factor and a weighted factor , and obtain a stationarytwo-step implicit iterative method. The range of the factors which guarantee theconvergence of iteration is explored.We also study the convergence properties and ratesfor both non-perturbed andperturbed equations.An implementable algorithm is presented by using Morozov discrepancy principle.The theoretical results show that the convergence rates of the new methods always lead to optimal convergentrates which are superior to those of the original one after choosing suitable relaxation and weightedfactors. Numerical examplesare also given, which coincide well with the theoretical results.     

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     

The credibility premiums for exponential principle

In the classical credibility theory, the credibility premium is derived on the basis of pure premium. However, the insurance practice demands that the premium must be charged under some adaptable premium principle and serves the purpose for insurance business. In this paper, the balanced credibility models have been built under exponential principle, and the credibility estimator of individual exponential premium is derived. This result is also extended to the versions of multitude contracts, and the estimation of the structure parameters is investigated. Finally, the simulations have been introduced to show the consistency of the credibility estimator and its differences from the classical one.     

汽车保险中的BMS

ＢＭＳ在汽车保险中的应用是十分广泛的．本文讨论了如何在汽车保险中更有效地应用ＢＭＳ的方法,包括三部分：第一部分评介了基于索赔次数模型的最优ＢＭＳ;第二部分提出了公平ＢＭＳ的方法并讨论了其性质;第三部分分析了如何在ＢＭＳ中不仅考虑索赔次数而且考虑索赔额之大小,这里假设给定个体保单的索赔额服从参数为θ的指数分布,而保单组合关于θ的结构函数为伽玛分布．     

保险精算中的一个随机模型

本文假设投保人到达保险公司的过程是一个强度为λ（ｘ）的非齐次Ｐｏｉｓｓｏｎ 过程、在时间区间（０,ｔ］中的索赔额是一个与保险规则及在（０,ｔ］中的投保人数有关的随机变量,提出一个新的保险精算模型,获得保险公司在（０,ｔ］中盈余额的一些数字特征．经典的个体模型和短期聚合风险模型均为本模型的特殊情形．     

双二项风险模型的破产概率

经典的复合二项风险模型是假定保险公司按照单位时间常数速度收取保费 ,本文在考虑保费收取次数服从二项分布的基础上讨论盈余的性质 ,并给出关于破产概率的一个定理 ,得到破产概率的一个上限     

不完全信息环境下具有随机工资和保费返还条款的DC养老金均衡策略

在不完全信息环境下,文章研究了具有随机工资和保费返还条款,且面临通胀风险的DC养老金均衡投资策略.假设养老金参与者连续不断地将其随机工资的固定比例作为保费缴纳到自己的养老金账户,基金经理将保费投资于一个无风险资产,一支股票和一支通胀指数债券以使养老金保值增值.其中股票预期收益率是随机的,并遵循均值回复过程,但基金经理无法直接观测.由于考虑了保费返还条款,则在累积期间死亡的参与者可提取按预先设定利率累积的保费.基金经理的决策目标是使每个幸存参与者养老金的终端价值期望最大化,并最小化终端价值的方差.利用滤波技术和纳什均衡框架,文章得到了DC养老金均衡策略和均衡值函数的解析式.最后,数值算例表明保费返还条款和信息损失都会使基金经理对风险投资更谨慎,但是保费返还条款对通胀指数债券均衡策略的影响更显著,而信息损失对股票均衡策略的影响更显著.     

Optimal Reinsurance with Probabilistic Constraints under Distortion Risk Measure北大核心CSCD

We follow Cheung and Lo [Scandinavian Actuarial Journal] and Chi et al. [Insurance: Mathematics and Economics] to investigate the optimal reinsurance problem where risks of the insurer is measured by distortion risk measures, and premiums are calculated under the generalized distortion premium principle. Our novelty is the inclusion of constraints on the maximum level of risk the reinsurer can tolerate. Our objective is to seek for all the optimal reinsurance strategies which minimize the insurer’s risk measurement of its total loss under the stipulated constraints. © 2022 Chinese Academy of Sciences. All rights reserved.