Optimal reinsurance under the α-maxmin mean-variance criterion

This paper studies an optimal reinsurance problem under the α-maximin mean-variance criterion proposed in Li et al. (2016). We generalize (Li et al., 2016) by considering a full range of ambiguity preferences and allowing for general form reinsurance contracts. For equilibrium reinsurance strategies, we find that the excess-of-loss form is unique for ambiguity-averse preferences but may not be optimal or unique for ambiguity-loving preferences. An insurer who is more ambiguous to the reference measure retains less risk if she is ambiguity-averse but does not necessarily retain more risk if she is ambiguity-loving and her ambiguity level is high. Our finding suggests that a highly ambiguity-loving preference may only manifest when the ambiguity level is very low, and hence, consistent with empirical studies, demonstrates that decision makers can be ambiguity-loving if they consider themselves more knowledgeable or competent than the other players.