Academic Report of School of Mathematical Sciences [2025] No. 130  

(Series Report for High-Level University Construction No. 1232)  

Title: Asymptotic Analysis of a Dynamic Systemic Risk Measure in a Renewal Risk Model  

Speaker: Professor Li Jinzhu (Nankai University)  

Time: 15:00–16:00, November 22, 2025 (Saturday)  

Location: Room 2433, Huiwen Building  

Abstract:  

In the context of insurance, we propose a dynamic systemic risk measure based on a multi-dimensional renewal risk model to describe the instant expected shortfall of an insurer at the moment when one of its business lines suffers a crisis (i.e., deficit). The asymptotic behavior of the measure is studied in both the asymptotic independence and asymptotic dependence cases, and some asymptotic formulas with uniformity over the entire time horizon are derived when the claim size distributions belong to the class of regular variation. The obtained results do not depend on specific setups of the renewal claim-number process, and they are also insensitive to specific dependence structures in the asymptotic independence case. These facts make our results concise in form and flexible in application. More interestingly, our results for the corresponding discounted version of the measure are independent of the time variable. Hence, the discounted version of the measure can be regarded approximately as a static (i.e., time-invariant) risk measure of the dynamic system.  

Speaker Biography:  

Li Jinzhu is a Professor and Doctoral Supervisor at the School of Mathematical Sciences, Nankai University. His research primarily focuses on stochastic processes and their applications in finance and insurance. He is currently presiding over one General Program of the National Natural Science Foundation of China. He has published over 30 academic papers in mainstream journals such as Advances in Applied Probability, Bernoulli, Insurance: Mathematics and Economics, Scandinavian Actuarial Journal, and ASTIN Bulletin.  

All faculty and students are welcome!  

Host: Li Jingchao  

School of Mathematical Sciences  

November 20, 2025