Risk and Duality in Multidimensional Stochastic Recursions

研究重点是将一维保险风险模型和一维随机内容模型之间的对偶理论推广到多维排队网络、库存网络、多人口和多收入来源模型中，从而得出计算重要利息概率的上界和下界。随机内容模型，如库存、流体、存储、水库和排队模型，在模型的状态空间可以用非负实数表征的特殊情况下，与保险风险模型具有优雅的对偶性。为了处理网络、多种群和多源模型，有必要将这种二元性扩展到多维状态空间情况。预计这种对偶性将有助于创建多维风险过程的一般理论（目前还不存在），并且将该理论应用于保险、商业、人口、库存、排队等将非常有用。

Sigman 9622657 Research centers on the generalization of the duality theory between one dimensional insurance risk models and one-dimensional stochastic content models to multidimensional queueing network, inventory network, multi-population, and multiple income source models, leading to upper and lower bounds for computing important probabilities of interest. Stochastic content models such as inventory, fluid, storage, reservoir and queueing models are already known to share an elegant duality with insurance risk models in the special case when the state space of the models can be characterized by non-negative real numbers. To handle network, multi-population and multi-source models, it is necessary to expand this duality to the multi-dimensional state-space cases. It is expected that such a duality would contribute to the creation of a general theory for multi-dimensional risk processes (which currently does not exist) and applications of this theory to insurance, business, population, inventory, queueing, etc., would be extremely useful.