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This article explores an individual’s optimal insurance choice and an insurer’s optimal product mix consisting of whole lifeinsurance and deferred life annuities in a market equilibrium framework. On the demand side, the insured decides an optimalinsurance choice by maximizing lifetime expected utility. On the supply side, an insurer chooses an optimal product mix by mini-mizing the conditional value-at-risk (CVaR) in its lines of business. By varying the loading for each insurance product, we matchdemand and supply of these products to clear the market. Our results suggest that market equilibria may occur when life insur-ance loading is relatively high and annuity loading is relatively low. This calls for attention from insurance regulators and lifeinsurers to review insurance/annuity underwriting and pricing.
Bibliographical noteWei Zhu acknowledges financial support from the Beijing Municipal Social Science Foundation (grant no. 17YJC039),the Fundamental Research Funds for the Central Universities in UIBE (grant no. ZD6-02), and the Program forDistinguished Young Talents at UIBE (Grant No. 20JQ05), and technical support from the Scientific Research CloudProject in the School of Insurance and Economics at UIBE. Jin Gao acknowledges financial support from the Direct Grant(DR19B1/101108) at Lingnan University.
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