Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps

This paper considers a robust optimal excess-of-loss reinsuranceinvestment
problem in a model with jumps for an ambiguity-averse insurer
(AAI), who worries about ambiguity and aims to develop a robust optimal
reinsurance-investment strategy. The AAI’s surplus process is assumed to
follow a diffusion model, which is an approximation of the classical risk
model. The AAI is allowed to purchase excess-of-loss reinsurance and invest
her surplus in a risk-free asset and a risky asset whose price is described by
a jump-diffusion model. Under the criterion for maximizing the expected
exponential utility of terminal wealth, optimal strategy and optimal value
function are derived by applying the stochastic dynamic programming
approach. Our model and results extend some of the existing results in
the literature, and the economic implications of our findings are illustrated.
Numerical examples show that considering ambiguity and reinsurance
brings utility enhancements.