日程安排

学术报告题目和摘要

Superpersition principle for nonlocal Fokker-Planck operators

张希承（武汉大学）

We prove the superposition principle for probability measure solutions to non-local Fokker-Planck equations, which in turn yields the equivalence between martingale solutions for SDEs with jumps and non-local PDEs with rough coefficients. As an application, we obtain a probabilistic representation for the strong solution of fractional porous media equations. (This is a joint work with Michael Rockner and Longjie Xie).

肿瘤细胞可塑性的数学模型及其推断

周达（厦门大学）

肿瘤细胞可塑性是近年来生物医学关注的热点问题之一。在本报告中，我们将介绍肿瘤细胞可塑性的一些数学模型，并结合肿瘤细胞系的实验数据讨论模型选择和参数估计等方面的统计推断问题。

Optimal reinsurance with reinsurer's risk limit under general premium principles

胡亦钧（武汉大学）

In this talk, we will discuss an optimal reinsurance models with reinsurer’s risk limit constraint and with the ceded loss functions being increasing and Lipschitz continuous.  We will also assume that the reinsurance premium principles satisfy three mild properties. Under the optimality criteria of minimizing the risk-adjusted value of the insurer’s liability based on VaR and CVaR risk measures, respectively, we deduce the optimal reinsurance treaties for the wide class of reinsurance premium principles, which are three-layer reinsurance treaties. In addition to the aforementioned three properties, if the reinsurance premium principle satisfies some additional mild conditions, we further demonstrate that two-layer reinsurance treaties are always optimal. Finally, as examples, when the reinsurance premium principle is specified to the expectation premium principle, the explicit optimal reinsurance treaties are also given. The results obtained significantly generalize some known results in the literature. (This talk is based on a joint work with Dr. Linxiao Wei)

Lack-of-Partial-Memory and Aging Properties of Multivariate Generalized Marshall-Olkin Distributions

林建华（厦门大学）

In this study the multivariate generalized Marshall-Olkin distribution is found to be of the lack-of-partial-memory property, somewhat similar to the lack-of-memory property of the multivariate Marshall-Olkin exponential distribution. Based on such an interesting finding, we further investigate the behavior and dependence of such distributions.