×

Optimal portfolio choice in retirement with participating life annuities. (English) Zbl 1461.91258

Summary: This article derives optimal consumption, investment, and annuitization patterns for retired households that have access to German-style participating payout life annuities (PLAs), allowing for capital market risks as well as idiosyncratic and systematic longevity risks. PLAs provide guaranteed minimum benefits in combination with participation in insurers’ surpluses. Minimum benefits are calculated based on conservative assumptions regarding capital market and mortality developments, while surpluses distributed to annuitants bridge the gap between the insurers’ actual investment and mortality experiences and the projections used in pricing. Through the participation scheme, systematic longevity risk is shared between insurers and annuitants, as unanticipated longevity shocks result in benefit adjustments via the surplus mechanism. We show that the retiree draws substantial utility from access to PLAs, equivalent to 20% of initial wealth in the presence of systematic longevity risk. We also find that stochasticity in mortality rates only has minor impact on the appeal of PLAs to the retiree. Even if the interest rate guarantee is reduced to zero in adverse capital market environments, PLAs prove to provide substantial utility for retirees. Overall, the participating life annuity design produces substantial welfare gains over a no-annuity world, while being an effective setup that helps providers manage long-term risks that are difficult to hedge otherwise, such as systematic longevity risks.

MSC:

91G05 Actuarial mathematics
91G10 Portfolio theory
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[1] Ballotta, L., A Lévy process-based framework for the fair valuation of participating life insurance contracts, Insurance: Mathematics and Economics, 37, 2, 173-96 (2005) · Zbl 1125.91060
[2] Barbarin, J.; Devolder., P., Risk measure and fair valuation of an investment guarantee in life insurance, Insurance: Mathematics and Economics, 37, 2, 297-323 (2005) · Zbl 1125.91061
[3] Bauer, D.; Kiesel, R.; Kling, A.; Ruß., J., Risk-neutral valuation of participating life insurance contracts, Insurance: Mathematics and Economics, 39, 2, 171-83 (2006) · Zbl 1098.91067
[4] Berdin, E.; Gründl., H., The Effects of a low interest rate environment on life insurers, Geneva Papers on Risk and Insurance—Issues and Practice, 40, 3, 385-415 (2015)
[5] Bohnert, A.; Gatzert., N., Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective, Insurance: Mathematics and Economics, 50, 1, 64-78 (2012) · Zbl 1235.91081
[6] Bohnert, A.; Gatzert., N., Fair valuation and risk assessment of dynamic hybrid products in life insurance: A portfolio consideration, Geneva Papers on Risk and Insurance—Issues and Practice, 39, 1, 148-72 (2014)
[7] Briys, E.; de Varenne., F., On the risk of life insurance liabilities: Debunking some common pitfalls, Journal of Risk and Insurance, 64, 4, 673-94 (1997)
[8] Bruszas, S.; Kaschützke, B.; Maurer, R.; Siegelin., I., Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?, Insurance: Mathematics and Economics, 78, 1, 230-45 (2018) · Zbl 1398.91317
[9] Cairns, A. J.; Blake, D.; Dowd., K., A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration, Journal of Risk and Insurance, 73, 4, 687-718 (2006)
[10] Eckert, J.; Gatzert, N.; Martin, M., Valuation and risk assessment of participating life insurance in the presence of credit risk, Insurance: Mathematics and Economics, 71, 1, 382-93 (2016) · Zbl 1371.91086
[11] Eling, M.; Holder., S., The value of interest rate guarantees in participating life insurance contracts: Status quo and alternative product design, Insurance: Mathematics and Economics, 53, 3, 491-503 (2013) · Zbl 1290.91085
[12] Gatzert, N.; Holzmüller, I.; Schmeiser., H., Creating customer value in participating life insurance, Journal of Risk and Insurance, 79, 3, 645-70 (2012)
[13] Gatzert, N.; Huber, C.; Schmeiser., H., On the valuation of investment guarantees in unit-linked life insurance: A customer perspective, Geneva Papers on Risk and Insurance—Issues and Practice, 36, 1, 3-29 (2011)
[14] Gatzert, N.; Kling., A., Analysis of participating life insurance contracts: A unification approach, Journal of Risk and Insurance, 74, 3, 547-70 (2007)
[15] Grosen, A.; Jørgensen., P. L., Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options and bonus policies, Insurance: Mathematics and Economics, 26, 1, 37-57 (2000) · Zbl 0977.62108
[16] Grosen, A.; Jørgensen., P. L., Life insurance liabilities at market value: An analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework, Journal of Risk and Insurance, 69, 1, 63-91 (2002)
[17] Horneff, V.; Kaschützke, B.; Maurer, R.; Rogalla., R., Welfare implications of product choice regulation during the payout phase of funded pensions, Journal of Pension Economics and Finance, 13, 3, 272-96 (2014)
[18] Horneff, V.; Maurer, R.; Mitchell, O. S.; Rogalla., R., Optimal life cycle portfolio choice with variable annuities offering liquidity and investment downside protection, Insurance: Mathematics and Economics, 63, 1, 91-107 (2015) · Zbl 1348.91147
[19] Horneff, W.; Maurer, R.; Mitchell, O. S.; Stamos., M., Asset allocation and location over the life cycle with survival-contingent payouts, Journal of Banking and Finance, 33, 9, 1688-99 (2009)
[20] Horneff, W.; Maurer, R.; Mitchell, O. S.; Stamos., M., Variable payout annuities and dynamic portfolio choice in retirement, Journal of Pension Economics and Finance, 9, 2, 163-83 (2010)
[21] Horneff, W.; Maurer, R.; Stamos., M., Optimal gradual annuitization: Quantifying the costs of switching to annuities, Journal of Risk and Insurance, 75, 4, 1019-38 (2008)
[22] Horneff, W.; Maurer, R.; Stamos., M., Life-cycle asset allocation with annuity markets, Journal of Economic Dynamics and Control, 32, 11, 3590-612 (2008) · Zbl 1181.91291
[23] Huang, H.; Milevsky., M. A., Portfolio choice and mortality-contingent claims: The general HARA case, Journal of Banking and Finance, 32, 11, 2444-52 (2008)
[24] Hubener, A.; Maurer, R.; Rogalla., R., Optimal portfolio choice with annuities and life insurance for retired couples, Review of Finance, 18, 1, 147-88 (2014) · Zbl 1417.91272
[25] Inkmann, J.; Lopez, P.; Michaelides., A., How deep is the annuity market participation puzzle?, Review of Financial Studies, 24, 1, 279-319 (2011)
[26] Inkmann, J.; Michaelides., A., Can the life insurance market provide evidence for a bequest motive?, Journal of Risk and Insurance, 79, 3, 671-95 (2012)
[27] Jørgensen, P. L., On accounting standards and fair valuation of life insurance and pension liabilities, Scandinavian Actuarial Journal, 2004, 5, 372-94 (2004) · Zbl 1087.62117
[28] Kling, A.; Richter, A.; Ruß., J., The impact of surplus distribution on the risk exposure of with-profit life insurance policies including interest rate guarantees, Journal of Risk and Insurance, 74, 3, 571-89 (2007)
[29] Maurer, R.; Mitchell, O. S.; Rogalla, R.; Kartashov., V., Lifecycle portfolio choice with systematic longevity risk and variable investment-linked deferred annuities, Journal of Risk and Insurance, 80, 3, 649-76 (2013)
[30] Maurer, R.; Rogalla, R.; Siegelin., I., Participating payout life annuities: Lessons from Germany, ASTIN Bulletin, 43, 2, 159-87 (2013) · Zbl 1292.91093
[31] Milevsky, M. A.; Young., V. R., Annuitization and asset allocation, Journal of Economic Dynamics and Control, 31, 9, 3138-77 (2007) · Zbl 1163.91440
[32] Reuß, A.; Ruß, J.; Wieland., J., Participating life insurance products with alternative guarantees: Reconciling policyholders’ and insurers’ interests, Risks, 4, 2, 1-18 (2016)
[33] Schmeiser, H.; Wagner., J., A joint valuation of premium payment and surrender options in participating life insurance contracts, Insurance: Mathematics and Economics, 49, 3, 580-96 (2011) · Zbl 1228.91048
[34] Schmeiser, H.; Wagner., J., A proposal on how the regulator should set minimum interest rate guarantees in participating life insurance contracts, Journal of Risk and Insurance, 82, 3, 659-686 (2015)
[35] Wolfsdorf, K., Versicherungsmathematik, Teil 1 Personenversicherungsmathematik (1997), Stuttgart, Germany: Teubner, Stuttgart, Germany
[36] Zaglauer, K.; Bauer., D., Risk-neutral valuation of participating life insurance in a stochastic interest rate environment, Insurance: Mathematics and Economics, 43, 1, 29-40 (2008) · Zbl 1140.91431
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.