Stackelberg differential game for insurance under model ambiguity: general divergence

Abstract

We solve a Stackelberg differential game between a buyer and a seller of insurance policies, in which both parties are ambiguous about the insurable loss. Both the buyer and seller maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a general divergence that measures the players' ambiguity, we obtain the Stackelberg equilibrium semi-explicitly. Our main results are that the optimal variance loading equals zero and that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability. Both of these important results generalize those we obtained in [Cao, J., Li, D., Young, V. R. & Zou, B. (2022). Stackelberg differential game for insurance under model ambiguity. Insurance: Mathematics and Economics, 106, 128–145.] under squared-error divergence.