Asymptotic analysis of a Stackelberg differential game for insurance under model ambiguity

We consider the problem of to which extent a diffusion process serves as a valid approximation of the classical Cramér-Lundberg (CL) risk process for a Stackelberg differential game between a buyer and a seller of insurance. We show that the equilibrium for the diffusion approximation equals the limit of the equilibrium for the scaled CL process, and it is nearly optimal for the pre-limit problem. Specifically, if the loss process follows a CL risk process and ambiguity is measured via entropic divergence, then the Stackelberg equilibrium of the diffusion approximation with squared-error divergence approximates the equilibrium for the former model to order $ \mathcal {O}\big (\frac {1}{\sqrt {n}}\big ) $ O(1n), in which we scale the CL model via n, as in Cohen and Young [(2020). Rate of convergence of the probability of ruin in the Cramér-Lundberg model to its diffusion approximation. Insurance: Mathematics and Economics 93: 333–340].