退保因素下保费收入为复合Poisson过程的风险模型

研究了一类风险过程,其中保费收入为复合Poisson过程,描述索赔及退保的计数过程分别为保单到达过程的P-稀疏过程与q-稀疏过程.运用鞅方法得出了破产概率满足的Lundberg不等式和一般公式,并通过数值计算分析了初始资本、期望理赔额及理赔比例、退保比例对保险公司破产概率的影响.

Abstract：

In this article, a risk model is considered where premium income follows compound Poisson processes. The arrival of the claims and the occurrence of the refunding are described as a p-thinning processes and q-thinning processes. By applying the martingale approach, the Lundberg inequality and the formula of the ruin probability are obtained. The effects of initial capital, expected claim amounts, proportions of the claim and the refunding on the ruin probability of the insurance company are analyzed by numerical computation.     

一类对偶平坦且具有迷向S 曲率的(α,β)度量

主要研究了一类特殊的(α,β)-度量F=αφ(s),s=β/α,其中φ(s)是关于s的k(k≥2)次多项式,α是一个Riemann度量,β是一个1-形式.得到了如下结果:F是对偶平坦的度量且具有迷向S-曲率的充分必要条件是F是Minkowski度量.