The Behavioral Economics of Insurance

We focus on four stylized facts of behavior under risk. Decision makers: (1) Overweight low probabilities and underweight high probabilities. (2) Ignore events of extremely low probability and treat extremely high probability events as certain. (3) Buy inadequate insurance for very low probability events. (4) Keeping the expected loss fixed, there is a probability below which the take-up of insurance drops dramatically. Expected utility (EU) fails on 1-4. Existing models of rank dependent utility (RDU) and cumulative prospect theory (CP) satisfy 1 but fail on 2, 3, 4. We propose a new class of axiomatically-founded probability weighting functions, the composite Prelec weighting functions CPF) that simultaneously account for 1 and 2. When CPF are combined with RDU and CP we get respectively, composite rank dependent utility (CRDU) and composite cumulative prospect theory (CCP). Both CRDU and CCP are able to successfully explain 1-4. CCP is, however, more satisfactory than CRDU because it incorporates the empirically robust phenomena of reference dependence and loss aversion.