Optimal investment and per-loss reinsurance strategies under a dynamic contagion claims process

We study the optimal investment and per-loss reinsurance problem for an insurer in a financial market with stochastic factors, where claim arrivals are governed by a dynamic contagion process. The claim intensity incorporates exogenous shocks, endogenous self-excitation, and stochastic fluctuations, thereby capturing the clustering behavior of insurance claims. The market price of risk is described by an affine diffusion factor process, which includes the geometric Brownian motion model and several stochastic volatility models as special cases. Using the dynamic programming approach, we derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and establish a verification theorem for general utility functions. Under exponential utility, we further obtain explicit expressions for the optimal investment strategy, the optimal per-loss reinsurance strategy, and the value function, and reduce the required technical conditions to exponential integrability conditions. Numerical examples for the 3/2 and 4/2 models show that both claim clustering and stochastic volatility have significant effects on the insurer’s optimal investment and per-loss reinsurance strategies.