报告人：教授

Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07604, USA

报告题目：关于相依性与随机序的系列报告

报告分以下四个主题：

1.    Generalized Marshall–Olkin distributions and related bivariate aging properties

Abstract: A class of generalized bivariate Marshall–Olkin distributions, which includes as special cases the Marshall–Olkin bivariate exponential distribution and the Marshall–Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with properties related to evolution of dependence along time, are investigated for this class of distributions. Extensions of results previously presented in the literature are provided as well.

时间:2018年06月11日下午2:30

地点：海韵教学楼306

2.    On Optimal Capital Allocation to Actuarial Risks

Abstract: The risk averse insurer always allocates the capital to its business units so as to minimize the aggregate loss in the sense of the increasing concave order. In the literature on actuarial science, there are lots of discussions on the form of the optimal capital allocation; however, few of them addressed the way to come up with the optimal allocation of the capital. In this study we apply stochastic optimization (mean-risk analysis and sample average approximation) to locate the optimal capital allocation. Some numerical examples are presented as illustrations.

时间:2018年06月12日下午2:30

地点：海韵教学楼306

3.    Preservation of WSAI under Default Transforms with Application in Asset Allocation for Dependent Realizable Returns

Abstract: Financial instruments traded in the market are usually subject to mutually dependent default risks, and a default does not  always make a zero return for the concerned risk asset. This paper revisits the portfolio selection problem on assets exposed to dependent default risks. To better model the general default mechanism, we introduce generalizations for the threshold model and the independence model of Cheung and Yang (2004) by assuming that a default incurs a smaller realizable return instead. By utilizing techniques of stochastic arrangement increasing random variables, we develop sufficient conditions to order the optimal assets allocations in the two generalized models. Some examples of dependence structures satisfying the sufficient conditions are presented as illustration as well.

时间:2018年06月13日下午2:30

地点：海韵实验楼108

4.    Stochastic Orders in Network Security

Abstract: Network science has attained rapid development during the past two decades. Since most work in this area rely heavily on experiments and simulations, it is urgent to develop nice models so as to gain insight on how the structure of a network has impact on the security issues.  This talk introduces two stochastic models on certain networks, in which the famous k-out-of-n tolerant structure is firstly employed to characterize a node's behavior. Based upon them, we draw the following two illuminating conclusions:  (i) A P2P network with the node's lifetime having more NWUE-ness is more resilient in the sense of having smaller isolation probability and longer durable time.  (ii) The probability for the node of a vulnerable network to be compromised increases as the degree of the network grows in the increasing convex order. The two conclusions are consistent to what computer scientists have observed in either practical situations or experiment studies. Since the models proposed herewith greatly extend those in literature, the two theoretical results carry an insight on both designing a more secure system and enhancing the security of an existing system.

时间:2018年06月14日下午2:30

地点：海韵实验楼108

联系人：林建华助理教授

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