Paper
Asymptotics of Systemic Risk in a Renewal Model with Multiple Business Lines and Heterogeneous Claims
Authors
Bingzhen Geng, Yang Liu, Hongfu Wan
Abstract
Systemic risk is receiving increasing attention in the insurance industry. In this paper, we propose a multi-dimensional Lévy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a business line of an insurer. We use the systemic expected shortfall (SES) and marginal expected shortfall (MES) defined with a Value-at-Risk (VaR) target level as the measurement of systemic risk. Assuming that all the claim sizes are pairwise asymptotically independent (PAI), we derive asymptotic formulas for the tail probabilities of discounted aggregate claims and the total loss, which hold uniformly for all time horizons. We further obtain the asymptotics of the above systemic risk measures. The main technical issues involve the treatment of uniform convergence in the dynamic time setting. Finally, we perform a detailed Monte Carlo study to validate our asymptotics and analyze the impact and sensitivity of key parameters in the asymptotic expressions both analytically and numerically.