Optimal asset allocation and reinsurance problem under enhanced dynamic contagious processes

Details

• Time: 18:30-19:30 pm  (Beijing Time)
• Date: Tuesday, April 2, 2024
• Venue: Tencent Meeting Room: 457-965-223
• Speaker： Dr. Guo Liu, Swansea University
  
• Host: Dr. Ran Xu

Abstract

In this paper, we deal with an insurer's optimal asset allocation and reinsurance policies. The financial market is assumed to consist of one risk-free asset and one risky asset. The insurer has two business lines, where the claim process for ordinary insurance business is assumed to follow a compound Poisson process, and the claim process for catastrophic insurance business is assumed to follow a compound dynamic contagious process. The dynamic contagious process, which is a generalization of the externally exciting Cox process with shot-noise intensity and the self-exciting Hawkes process, is enhanced by accommodating the dependency structure between the magnitude of contribution to intensity after initial events for catastrophic insurance products and its claim/loss size.  We also consider the dependency structure between the positive effect on the intensity and the negative crashes on the risky financial asset when initial events occur. Under these specifications, we investigate an optimization objective that maximizes the expected utility of the insurer's terminal surplus. By constructing the extended Hamilton-Jacobi-Bellman (HJB) equation with the dynamic programming principle, the optimal reinsurance policy w.r.t. ordinary claims is derived explicitly and an iterative scheme is developed to solve the value function and the optimal asset allocation policy and the reinsurance policy w.r.t. catastrophic claims numerically. Furthermore, the proof of convergence of the iterative method is provided rigorously. Finally, we present numerical examples to demonstrate the impact of key parameters.

Speaker

Guo Liu, Ph.D., is a Lecturer of Actuarial Science at Swansea University. He received his Ph.D. degree in Actuarial Science from the University of Melbourne. His research expertise centers on stochastic optimal controls, portfolio choice, life-cycle planning, dividend problems， climate risks, and point processes. He has published in top-tier journals including Insurance: Mathematics and Economics, European Journal of Operational Research, and Finance Research Letters.