A Unified Framework for Insurance Demand and Mortality Immunization

Abstract

This paper explores an individual’s optimal insurance choice and an insurer’s optimal product mix consisting of whole life insurance and deferred annuity under the tâtonnement framework. On the demand side, the insured decides an optimal insurance choice by maximising lifetime expected utility. On the supply side, an insurer chooses an optimal product mix by minimising the Conditional Value-at-Risk (CVaR) of losses in its lines of business. By varying the loading factor for each insurance product, we match the demand and the supply of these products to clear the market. Our results show that market equilibriums occur when life insurance loading is relatively high and annuity loading is relatively low. This calls for attentions for insurance regulators and insurance companies to re-examine insurance/annuity underwriting and pricing. Our results also help explain the annuity puzzle and the life insurance puzzle in a neoclassic economic framework.