Insurer Investment, Life Insurance Policy Choices, and Policy Surrender

ABSTRACT

This study develops a contingent framework to examine the contract issuance of alternative unit-linked insurance plans (ULIPs) considering policy surrender. We show that the extension of the aggressive/conservative-plan policy surrender date enhances policyholder protection and insurer default risk when the two optimal guaranteed rates of the programs remain fixed. Increasing aggressive-plan policy surrenders improves policyholder protection and insurer survival when the optimal invested-asset interest rate remains unchanged. Increasing conservative-plan policy surrenders negatively impacts policyholder protection but supports insurer survival. Our results complement the literature by demonstrating that ULIPs are relevant to policyholder protection and insurer survival in the asset-liability matching management.

KEYWORDS:

• Unit-linked insurance plans
• policy surrender options
• policyholder protection
• insurer survival

JEL:

• G13
• G22

Acknowledgements

The authors would like to thank the subject editor and two anonymous referees for their helpful comments and suggestions. The usual disclaimer applies. Funding This work was supported by the National Social Science Fund of China under Grant 21XJY006 (Shi Chen).

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1. Source for Europe: https://www.insuranceeurope.eu. Source for Luxembourg: https://www.aca.lu.

2. The paper remains silent on the coronavirus COVID-19 issue (for example, Lin, Chang, and Chen 2021; Wang et al. 2020) and life insurance policy loans (Li, Xie, and Lin 2021).

3. Five factors are claim settlement ratio, solvency ratio, ULIPs performance, policy charges, and investment strategies. Ten operative charges of ULIPs are fund management charge, administration charge, switch charge, mortality charge, surrender charge, partial withdrawal charge, premium allocation charge, guarantee charges, premium charges, and rider charges.

4. See Poufinas and Michaelide (2018) for the determinants of life insurance policy surrenders.

5. Brockman and Turtle (2003) derive the formula for corporate security valuation based on path-dependent barrier option models. The conceptual framework of Brockman and Turtle (2003) can be expressed mathematically in the closed-form DOC valuation model of Merton (1973).

6. Briys and de Varenne (1994) develop a contingent claim model to evaluate the equity and liabilities of a life insurance company. Grosen and Jørgensen (2002) extends the model of Briys and de Varenne (1994) by introducing a regulatory mechanism, and show that the regulation makes the various claims on the insurer’s assets become more exotic and obtain barrier option properties. Cheng and Li (2018) further study the risk-neutral valuation of participating life insurance policies with surrender guarantees when an early default mechanism.

7. This behavior mode has been modeled by Hong and Seog (2018).

8. Our model deals with a firm-level numerical analysis. It is not easy to well-defined a cross-sectional dataset for our numerical analysis. This paper collects data from related studies to approaching the case in reality. The data collection across different years is a limit to our analysis.

9. There are three functions to reflect the market structures of the model. The loci include ($R_A,A$), ($R_h,L_h$), and ($R_l,L_l$). The first one is the demand function the insurer faces, and the last two are the supply functions. The interest rate of the risky asset relies on an empirical finding, and its corresponding quantity is arbitrary. We develop alternative bundles for the demand function used in our numerical analysis according to the initial bundle. The same patterns apply to the supply functions.

10. There is no specific reason to assume the liquid-asset interest rate at 3.50, approaching 3.10%, but not hurting the qualitative solutions. However, our model holds when $R_A>R_h>R_B>R_l$.

11. When the differences are considered, the model will create a much more complicated expression but will have the same qualitative effects on the parameters we want to focus on.

12. Poufinas and Michaelide (2018) pointed out that life insurance policyholders may need the premium money or the accumulated savings to meet their urgent or short-term needs, so they lapse them when a surrender value exists. Besides, certain main macroeconomic variables also affect policy surrenders, such as GDP per capita growth, unemployment, inflation, and long-term interest rate.