统计相依的精算风险管理中的资金分配问题的研究

The study of dependent notions have widely applications in financial engineering, insurance industry, enterprise risk management. This project establishes some sufficient conditions for some Archimedean copulas equipped with marginal distributions arranged in ascending usual stochastic order [likelihood ratio order] having weakly stochastic arrangement increasing (WSAI) [stochastic arrangement increasing (SAI)] property and some background risk models having SAI [WSAI, right tail weakly stochastic arrangement increasing (RWSAI), left tail weakly stochastic arrangement increasing (LWSAI)] property. On the other hand, in the framework of expected utility theory, this project focuses on argument increasing (AI) functions of a multivariate random vector and a real vector, which formulates more general frame to investigate allocation problem. To be specific, for RWSAI and LWSAI random vectors, we develop some results of stochastic comparisons for two total risks with two allocation vectors arranged in majorization order. To illustrate the power of our main results, we give some applications in the capital allocation problems of financial engineering, insurance industry, enterprise risk management, respectively. The study of this project would not only improve or extend the corresponding works in the literature, but also provide some more important information to estimate and control random risks.

随机向量的相依性研究在经济金融、保险精算、风险管理等诸多领域中有着广泛的应用。本项目研究利用特定类型的Arichimedean copula耦合按普通随机序（似然比随机序）递增排列的边际分布产生多维弱随机递增（随机递增）的随机向量以及建立某些类型的背景风险模型具有随机递增（弱随机递增、右尾弱随机递增、左尾弱随机递增）性质的充分条件。同时，在期望效用理论下，本项目借助增排函数将右尾弱随机递增（左尾弱随机递增）的随机向量和实向量连在一起建立一般分配模型；研究在此模型下总风险随分配策略按超优序变化而变化的规律，并将这些结论应用于经济金融、保险精算、风险管理等领域的资金分配问题中。本项目的研究不仅丰富和发展相依性理论与分配问题的相关结论，而且为投资者、精算师、风险管理者准确地评估和控制风险提供了一定的理论依据和技术支持。

随机向量的相依性研究在经济金融、保险精算、风险管理和可靠性等诸多领域中有着广泛的应用。本项目主要研究n中取k系统的工作元件具有左尾置换递减相依性下冗余元件的分配问题。对于匹配冗余元件寿命具有随机递增排列相依性的情形，本项目建立了将可靠性较强的冗余元件分配给可靠性较弱的工作元件的策略较好。同时，对于冗余元件具有独立同分布的条件，本项目证明了可靠性较弱的工作元件应该多分配些冗余元件的策略有助于提高系统的寿命。本项目的研究不仅丰富和发展相依性理论与冗余分配问题的相关结论，而且为工程师准确地设计冗余系统提供了一定的理论依据和技术支持。