A Unified Framework for Mortality Immunization and Insurance Demand

Abstract

In this paper, we propose a unified framework to simultaneously examine an insurer’s mortality immunization strategy and individuals’ insurance demand. On the supply side, an insurer chooses an optimal product mix of whole life insurance and deferred annuity by minimising the Conditional Value-at-Risk (CVaR) of its portfolio loss. On the demand side, the insured decide an optimal insurance choice by maximising his or her expected lifetime utility. Using the tâtonnement approach, we match the demand and supply of these insurance products and thus determine the optimal prices to clear the market. Our model in a neoclassical economic framework helps explain a few stylized facts or puzzles in life insurance markets, e.g., simultaneous holding of life insurance and annuity, low annuitisation, and insufficient purchase of life insurance in the working age population. Our results show that market equilibria occur when life insurance loading is relatively high and annuity loading is relatively low. This calls for attentions from insurance regulators and insurance companies to re-examine insurance/annuity underwriting and pricing.