Doctoral Public Lecture | Duo Xu

Student Name: Duo Xu
Program: Statistics
Thesis Title: Drawdown-dependent surplus analysis and its applications in insurance valuation
Supervisor: Dr. Shu Li
Location: Western Science Centre 248

Abstract: 

Drawdown is a key measure of downside risk in surplus processes, widely studied in insurance and finance. This thesis focuses on drawdown-dependent surplus analysis and its applications in actuarial science.

In Section 2, we investigate a drawdown-dependent fee structure in the context of ultimate drawdown insurance and analyze the fair value of such contracts. By incorporating a surrender option, we identify the optimal surrender strategy under the proposed fee structure. Our results show that, compared to a constant fee, the drawdown-dependent fee reduces the incentive for policyholders to surrender.

In Section 3, we turn to the valuation of variable annuities with the same drawdown-dependent fee structure. We derive explicit expressions under the proposed model and examine the impact of this structure on surrender incentives. The analysis provides valuable insights into how policyholders behave under different fee designs.

Section 4 extends the study by considering optimal surrender strategies for variable annuities. We introduce a two-threshold framework to model policyholder decisions and formulate the associated Hamilton–Jacobi–Bellman equation to characterize the value function. This builds on the previous section and further evaluates the influence of the fee structure on surrender behavior.

In Section 5, we generalize key identities involving the first-passage time, local time, and occupation time. We derive the two-sided exit joint Laplace transform for these drawdown-related quantities under a spectrally negative L\'evy process. Additionally, we obtain one-sided exit results as limiting cases. These theoretical results might be applied to the context of insurance valuation as well.

Please contact the Graduate Assistant in the program for further information: https://grad.uwo.ca/about_us/program_contacts.cfm.