When Effort Rimes with Advantageous Selection: A New Approach to Life Insurance Pricing

Abstract

This paper investigates the demand for and pricing of life insurance when insureds' risk aversion is correlated with their precautionary effort. We assume that the population is divided into two groups: (i) very risk-averse individuals who have a low probability of death (PoD) because of the precautionary effort they undertake and (ii) less risk-averse individuals who undertake less effort and thus have a higher PoD. After computing the pooling equilibrium price under perfect competition for a class of CRRA utility and bequest functions, we compute the level of demand for life insurance by the two groups. Under the assumption of negative correlation between risk aversion and risk exposure, lower-risk individuals still buy insurance even if the price offered is higher than the fair price corresponding to their group. This is because low risks are assumed to be more risk averse, valuing insurance so highly that they can tolerate higher than fair prices. We also present some cases when low-risk individuals purchase more than their high-risk neighbors even though they realize they are subsidizing the high risks. In such cases, the insurers gain the advantage of facing a PoD which is smaller than the rate they normally expect. This fact contradicts the so-called adverse selection hypothesis.