多维正相依再保险条约中最优自留向量的确定

发布时间：2018-08-23 18:43

【摘要】：为了探寻多维正相依风险在再保险业务中的最优自留额,应用条件极值理论,得到了依凸序最优自留向量满足的一般形式的方程组.在2维情形下,进一步应用单侧导数判断函数单调性,给出了最优解的显式表达式,并发现其可能取值的矩形域必为平面上的一个点.针对更高维情形,在自留损失方差最小与期望指数效用最大这两个特定准则下,假定索赔额分布属于对数正态分布族并依随机序正相依或者通过一个共同的指数分布正相依,分别给出了更易于求解的方程组.最后通过算例表明了所提方法的可行性与有效性.
[Abstract]:In order to find out the optimal retention amount of multi-dimensional positive dependent risk in reinsurance business, a general set of equations satisfying the optimal retention vector in convex order is obtained by applying the conditional extremum theory. In the case of 2-D, the explicit expression of the optimal solution is given by using the monotonicity of the one-sided derivative judgment function, and it is found that the rectangular region of its possible value must be a point on the plane. For higher dimensional cases, under the two special criteria of minimum variance of self-retention loss and maximum utility of expected exponent, it is assumed that the distribution of claim amount belongs to a family of logarithmic normal distributions and is positively dependent in random order or positively dependent by a common exponential distribution. The equations which are easier to solve are given respectively. Finally, the feasibility and effectiveness of the proposed method are demonstrated by an example.
【作者单位】：上海理工大学管理学院;淮北师范大学数学科学学院;
【基金】：国家自然科学基金资助项目(11171221) 安徽省高校优秀青年人才支持计划重点资助项目(gxyqZD2016104) 安徽省高等学校自然科学研究资助项目(KJ2014B18)
【分类号】：F840

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