On the threshold dividend strategy for a generalized jump-diffusion risk model

In this paper, we generalize the Cramér-Lundberg risk model perturbed by diffusion to incorporate jumps due to surplus fluctuation and to relax the positive loading condition. Assuming that the surplus process has exponential upward and arbitrary downward jumps, we analyze the expected discounted penalty (EDP) function of Gerber and Shiu (1998) under the threshold dividend strategy. An integral equation for the EDP function is derived using the Wiener-Hopf factorization. As a result, an explicit analytical expression is obtained for the EDP function by solving the integral equation. Finally, phase-type downward jumps are considered and a matrix representation of the EDP function is presented.     

Sensitivity of risk measures with respect to the normal approximation of total claim distributions

A simple and commonly used method to approximate the total claim distribution of a (possibly weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of convergence of the error relative to the number of clients, we specify the relative error’s asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.     

On the expected discounted penalty function for risk process with tax

In this paper we consider the generalized Cramér-Lundberg risk model including tax payments. We investigate how tax payments affect the behavior of a Cramér-Lundberg surplus process by defining an expected discounted penalty function at ruin. We derive an explicit expression for this function by solving a differential equation. Consequently, the explicit formulas for the discounted probability density function of the surplus immediately before ruin and the discounted joint probability density function of the surplus immediately before ruin and the deficit at ruin are obtained. We also give explicit expressions for the function for exponential claims.     

一类推广负风险和模型的破产概率

本文研究了带干扰的两险种负风险和模型的破产问题.利用无穷小方法,给出了该风险模型破产概率所满足的微分-积分方程,并推导出破产概率满足的Lundberg型不等式.最后指出了当索赔服从负指数分布时破产概率的上界,推广了经典风险模型的结果.     

常数红利边界下的一类马氏风险模型

本文研究了常数红利边界下一类马氏风险模型的红利派发矩,破产前所有红利的分布等相关问题.利用更新方法,给出了该模型破产前红利折现的期望满足的微分-积分方程,得到破产前所有红利的分布.通过构造特殊的初始条件,得到了相关的方程组解,推广了文献[3]的结果.     

An explicit model of default time with given survival probability

For a given filtered probability space (Ω,F,P), an F-adapted continuous increasing process Λ and a positive P-F local martingale N such that Λ₀=0 and N_te^−Λ_t≤1, we construct a probability measure Q^Z and a random time τ such that Q|_F∞=P|_F∞ and Q[τ>t|F_t]=Z_t. The probability Q^Z is linked with the well-known Cox model by an explicit density function. Various properties exist, which characterize Q^Z from others. Let G=(G_t)_t≥0 with G_t=F_t∨σ({τ≤s}:s≤t). We establish the (H^′)-property between the filtrations F and G, and we provide the enlargement of filtration formula.     

Incorporating ergonomic risks into assembly line balancing

In manufacturing, control of ergonomic risks at manual workplaces is a necessity commanded by legislation, care for health of workers and economic considerations. Methods for estimating ergonomic risks of workplaces are integrated into production routines at most firms that use the assembly-type of production. Assembly line re-balancing, i.e., re-assignment of tasks to workers, is an effective and, in case that no additional workstations are required, inexpensive method to reduce ergonomic risks. In our article, we show that even though most ergonomic risk estimation methods involve nonlinear functions, they can be integrated into assembly line balancing techniques at low additional computational cost. Our computational experiments indicate that re-balancing often leads to a substantial mitigation of ergonomic risks.     

多周期多目标条件风险值模型

在商业、工业、电力和房地产等行业中存在许多复杂的多周期风险决策问题,它的数学模型研究对于解决这些问题具有重要的作用.作者建立了一种新的多周期多目标条件风险值(CVaR)数学模型理论和方法.先定义了一种带时间段的多周期多目标损失函数下的α-VaR和α-CVaR值,给出了一类多周期多目标CVaR最优化模型.然后,证明了多目标意义下的对应模型的等价定理,给出了多周期多目标CVaR模型的近似求解等价模型.最后,建立了一种生产企业在供过于求和供不应求两种情形下产生的多周期双目标CVaR模型,针对一个电力生产企业进行的数值实验,表明了模型可以得到在最小供给的用电损失分布下的各周期下的相匹配供电策略,可以帮助供电部门各个时期供电不平衡状况下的风险控制.     

规定安全间隔的CNS性能环境研究

对平行航路下规定安全间隔的CNS性能环境评估问题进行了研究.首先分析了CNS性能环境对飞机碰撞风险的影响,并结合Reich模型和概率论方法建立了CNS性能环境下飞机纵向、侧向和垂直方向上的碰撞风险模型;其次对碰撞风险模型进行分析转化得到了规定的安全间隔和安全目标水平下CNS性能环境的评估计算方法.最后对平行航路的CNS性能环境进行了评估计算,得到符合航路安全目标水平1.5×10~(-8)的CNS性能环境为RNP10、RCP400、RSP20.     

水资源短缺风险因子的筛选模型

水资源短缺评价首先需要确定指标体系,投影寻踪模型与灰色关联度法相结合,可以有效地筛选出水资源短缺风险因子,为进一步进行风险评价奠定了基础,同时也为制定风险的防范措施和对策提供了理论依据.综合应用这两种模型,对北京市2001～2009年的水资源短缺风险进行研究,结果表明:降水量、日照时数、雨日数、单位GDP污水排放量、人均GDP、工业总产值占有率、污水处理率和水循环使用率这8个指标是北京市水资源短缺的主要风险因子.