讲座主题1：Copula-based Markov Process
摘要： Starting from a bivariate copula family,weinvestigate the existence of a Markov process whose temporal dependence is modeled by the given copula family. Due to that the transition function plays a core role for constructing a Markov process, a transition function should be defined from a copula family. For this purpose, the modified partial Dini derivatives of a bivariate copula are defined and applied for defining transition probabilities, and some properties of the modified partial Dini derivatives are proved. A necessary and sufficient condition for the family of the defined transition probabilities to be a transition function is provided. Given a bivariate copula family, a sufficient condition for the existence of a Markov process is provided, where the Markov process has a transition function generated by the modified partial Dini derivatives of the bivariate copula family and the temporal dependence of the Markov process is modeled by the given copula family. Moreover, under some assumptions the consistency of the bivariate copula family under the $*$ product operation is necessary and sufficient for the existence of a Markov process. Finally, paths of some typical copula-based Markov processes are simulated to show the importance of fitting the copula method into the framework of stochastic processes. It is a joint work with Jun Fang, Fan Jiang and Long Liu.
杨静平，北京大学数学科学学院教授，博士生导师。研究兴趣有金融和保险中的风险相依性、债券组合模型和信贷资产证券化等。在精算学的国际四大学术期刊、金融数学期刊Finance and Stochastics、SIAM Journal on Financial Mathematics、Journal of Computational Finance以及概率论期刊Bernoulli等发表了多篇学术论文。主持完成了中国国债发行策略的随机模拟模型、国债收益率曲线的拟合、信贷资产证券化以及含权债估值模型等方面的金融业课题。
讲座主题2：Optimal Investment Problem for a Hybrid Pension with Intergenerational Risk-sharing and Longevity Trend under Model Uncertainty
摘要：Thistalk discusses the optimal investment problem for a hybrid plan under model uncertainty, where both the contribution and the benefit are adjusted depending on the performance of the plan. Furthermore, an age and time-dependent force of mortality and a linear maximum age are considered to capture the longevity trend. Suppose that the plan manager is ambiguity averse and is allowed to invest in a risk-free asset and a stock. The plan manager aims to find optimal investment strategies and optimal intergenerational risk-sharing arrangements by minimizing the cost of unstable contribution risk, the cost of unstable benefit risk and discontinuity risk under the worst-case scenario. By applying the stochastic optimal control approach, closed-form solutions are derived under a penalized quadratic cost function. Through numerical analysis, we find that the intergeneration risk-sharing is achieved in our collective hybrid pension plan effectively. And it also shows that when people live longer, postponing the retirement seems a feasible way to alleviate the stress of the aging problem.
荣喜民，天津大学数学学院教授，博士生导师，天津市现场统计学会副理事长，中国工程概率统计学会常务理事。主要从事金融数学、精算数学、风险管理等方面研究工作，在IME、SAJ、QF、IMA Journal of Management Mathematics、JCAM、JMAA、JSSC、系统工程理论与实践等期刊发表相关论文近百篇，其中SCI检索40余篇。主持并参与多项国家自然科学基金和天津市自然科学基金项目。
讲座主题3：Generalized Optimized Certainty Equivalent with Applications in the Rank-dependent Utility Model
摘要：Classic optimized certainty equivalent (OCE), proposed by Ben-Tal and Teboulle (1986), employs the classical expected utility model to evaluate the random risk, in which model, each decision maker is characterized by a unique probability measure and only outcome uncertainty is assumed. Due to the lack of information, the distribution ambiguity or Knightian uncertainty prevails in reality. We employ the variational preference of Maccheroni et al. (2006) to address the issue and generalize the concept of OCE. In this talk, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on varphi-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of optimized certainty equivalent based on the rank-dependent utility (RDU) model. The dual representation of RDU-based shortfall risk measure proposed by Mao and Cai (2018) is also presented.
毛甜甜，博士，中国科技大学管理学院副教授，主要研究方向为风险度量、量化金融、保险风险管理、极值理论和随机占优及在决策理论中的应用等。曾获得首届国家博士学术新人奖和国际精算师协会2020年Bob Alting von Geusau奖。近年来在Insurance: Mathematics and Economics, Mathematical Programming, Mathematical Finance, Mathematics of Operations Research, Finance and Stochastic等期刊上发表40多篇论文，主持国家自然科学基金2项。
讲座主题4：Risk Aversion in the Presence of a Background Risk for State-dependent Bivariate Utility Functions
摘要：In thistalk, the relations between the state-dependent bivariate utility function and the risk aversion to one risk in the presence of a background risk under various dependent structures, such as the independent structure, the positively expectation-dependent structure and a general dependent structure, are discussed. A sufficient condition guaranteeing the preservation of risk aversion to one risk in the presence of a background risk for state-dependent utility function is provided. It is showed that using the common concept of bivariate risk aversion, the conditions implying the risk aversion in the presence of a background risk for state-independent bivariate utility functions are not applicable to the state-dependent case. Instead, these conditions imply a weaker version of bivariate risk aversion under the state-dependent bivariate utility, named as the risk aversion in the presence of a background risk for state-independent gambles. Another two new concepts of bivariate risk aversions, named as the uniform risk aversion in presence of a background risk and the uniform risk aversion in presence of a background risk for state-independent gambles are also introduced. We show that these conditions on the state-dependent bivariate utility function implying the risk aversion in the presence of a background risk for state-independent gambles are equivalent to the uniform risk aversion in the presence of a background risk for state-independent gambles. The equivalent conditions for the uniform risk aversion in the presence of a background risk under different dependent structures are also presented. Thistalk provides some new insights into the state-dependent preferences with two risks under various dependent structures.
谢杰华，教授、江西省杰出青年基金项目获得者，被聘为中国现场统计研究会风险管理与精算分会理事、中国工业与应用数学学会系统与控制数学专业委员会委员、江西省青年科技工作者协会会员。长期从事风险管理和精算、决策理论及方法、应用概率统计等多个领域的研究，在Insurance: Mathematics and Economics、ASTIN Bulletin等精算学领域权威期刊，Fuzzy Sets and Systems、Science in China、SIAM: Theory of Probability and Its Applications等数学领域的权威期刊以及Decision Analysis等Informs旗下知名决策科学期刊上发表论文多篇。主持国家自然科学基金项目3项，江西省杰出青年基金等省部级项目8项。