Academic Report of School of Mathematical Sciences [2026] No. 081
(Series Report for High-Level University Construction No. 1340)
Title：Vulnerable European and American Options Under a Risk Process Model
Speaker：Dr. Liu Ruyi (University of New South Wales)
Time：15:00-17:00, July 28, 2026
Location：Tencent Meeting:933705791
Abstract: Within the framework of hazard processes, this paper studies European and American fragile options that may experience exogenous termination under conditions of market incompleteness. We prove that the reduced-upper price of a European fragile option is equal to the unique price of an American option with a properly defined payoff, where the holder’s exercise time is restricted to a random set determined by the right support of the hazard process. For American fragile options, we prove that their upper-reduced price equals the price of an American option with no restrictions on the exercise time, while their lower-reduced price equals the price of a specific game option in which the issuer’s exercise time is restricted to the aforementioned random set.
Speaker Profile：Liu Ruyi is a tenured lecturer and Ph.D. advisor in the School of Mathematics and Statistics at the University of New South Wales, Australia. He received his Ph.D. in Science from Shandong University in 2020; from 2021 to 2024, he served as a postdoctoral researcher at the University of Sydney, Australia; in September 2024, he conducted visiting research at the Hong Kong Polytechnic University; and in July 2025, he was appointed to the School of Mathematics and Statistics at the University of New South Wales. His research interests include stochastic control, stock pair trading, and the pricing and hedging of interest rate derivatives. He has published more than ten academic papers in journals such as Automatica, SIAM Journal on Financial Mathematics, Finance and Stochastics, and Science China Mathematics.
Faculty and students are welcome to attend!
Invited by: Yuanzhuo Song
School of Mathematical Sciences
July 27, 2026
