Modern tontine with bequest: Innovation in pooled annuity products

Abstract

We introduce a new pension product that offers retirees the opportunity for a lifelong income and a bequest for their estate. Based on a tontine mechanism, the product divides pension savings between a tontine account and a bequest account. The tontine account is given up to a tontine pool upon death while the bequest account value is paid to the retiree's estate. The values of these two accounts are continuously re-balanced to the same proportion, which is the key feature of our new product.Our main research question about the new product is what proportion of pension savings should a retiree allocate to the tontine account. Under a power utility function, we show that more risk averse retirees allocate a fairly stable proportion of their pension savings to the tontine account, regardless of the strength of their bequest motive. The proportion declines as the retiree becomes less risk averse for a while. However, for the least risk averse retirees, a high proportion of their pension savings is optimally allocated to the tontine account. This surprising result is explained by the least risk averse retirees seeking the potentially high value of the bequest account at very old ages.

The modern tontine

“…In an expected-lifetime-utility context, Bernhardt and Donnelly [6] derive the optimal investment in a tontine that allows to bequeath payments in the case of death.…”

“…Furthermore, providers of pension products are exposed to the longevity risk of their customers, which can only be partially passed on to them. 6 Therefore, alternative solutions for providing pensions, long-term care and health insurance are needed.…”

“…5 See Berdin and Gründl [5]. 6 See, e.g., the legal provisions for profit participation for German life insurance products. There, 90% of mortality gains must be passed on to the policyholders, whereas mortality losses must be completely borne by the insurer; see §7 MindZV (profit participation regulation).…”

Longevity risk and capital markets: the 2018–19 update

“…Beard, 1971;McNown & Rogers, 1992;Christensen & Vaupel, 1996;Hanewald, 2011;Murphy & Di Cesare, 2012;Arnold & Sherris, 2015;Gourieroux & Lu, 2015;Alai et al, 2018;Boumezoued et al, 2018;Yue et al, 2018;Li et al, 2019;Lyu et al, 2020) • Longevity risk and financial innovation (improvements in the analysis and design of longevity-linked products) (e.g. Gong & Webb, 2010;Stevens at al., 2010;Richter & Weber, 2011;Cocco & Gomes, 2012;Brown & Warshawsky, 2013;Bernhardt & Donnelly, 2019) • Reverse or ERMs (e.g. Wang et al, 2008;Huang et al, 2011;Yang, 2011;Alai et al, 2014a;Kogure et al, 2014;Shao et al, 2015;Lee et al, 2018) • Longevity risk in investment portfolios (e.g.…”

Service Innovation of Insurance Data Based on Cloud Computing in the Era of Big Data

“…e former includes insurance consultation, underwriting physical examination, and other services, while the latter is the renewal service, filing, and claim settlement service provided by the insurance company after the customer has insured [2]. e core of insurance service is insurance protection, and insurance service has the characteristics of intangibility, interactivity, nonstorability, difference, integrity, and dual attributes [3].…”