Impact of Preferences on Optimal Insurance in the Presence of Multiple Policyholders

In the optimal insurance literature one typically studies optimal risk sharing between one insurer (or reinsurer) and one policyholder. However, the insurance business is based on diversification benefits that arise when pooling many insurance policies. In this paper, we first show that results on optimal insurance that are valid in the case of a single policyholder extend to the case of multiple policyholders, provided their insurance claims are independent. However, due to natural catastrophes, increasing life expectancy and terrorism events, insurance claims show tendency to be correlated. Interestingly, in the case of interdependent insurance policies, it may become optimal for the insurer to refuse selling insurance to some prospects, based on their attitude towards risk or due to their risk exposure characteristics. This finding calls for government policies to ensure that insurance stays available and affordable to everyone.