Annuities, long-term care insurance, and insurer solvency
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Annuities, long‑term care insurance, and insurer solvency Franca Glenzer1 · Bertrand Achou2 Received: 14 May 2018 / Accepted: 9 January 2019 / Published online: 19 March 2019 © The Geneva Association 2019
Abstract The market for long-term care (LTC) insurance is much smaller than economic theory predicts. One reason is that premium markups are prohibitively high. We aim at quantifying markups for LTC insurance due to mortality and morbidity risk. To this end, we model a shareholder value maximising insurance company that is subject to solvency regulation. Because liabilities from LTC insurance (which depend on future morbidity and mortality) are more volatile than liabilities from annuities (which only depend on future mortality), capital provisions to ensure compliance with regulatory solvency requirements are higher if an insurance company offers LTC insurance instead of annuities. At the same time, a higher volatility in the LTC insurance segment also implies a higher expected payoff to the insurance company’s shareholders. To quantify which effect prevails and which product policy is optimal, we conduct an empirically calibrated simulation study with stochastic mortality and LTC needs. Our results show that offering LTC insurance increases the upside potential to shareholders, but that effect is more than offset by a higher need for external capital. Consequently, if shareholders are to accept an LTC insurance segment, holders of an LTC insurance policy need to pay considerable markups. The more LTC insurance contracts the insurer has sold, the higher the markups. Keywords Longevity and morbidity risk · Long-term care insurance · Insurer solvency JEL classification G22 · G23 · G32 · J11
* Franca Glenzer [email protected] 1
Retirement and Savings Institute, HEC Montréal (Université de Montréal), Montréal, QC, Canada
2
Department of Economics, CIRRIS and Université Laval, Quebec, Canada
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Annuities, long‑term care insurance, and insurer solvency
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Motivation Life annuities and long-term care (LTC) insurance products are designed to offer protection against two of the most salient risks faced by today’s retirees: outliving one’s savings, and LTC expense risk. Because of population ageing and structural changes—such as the move from defined benefit to defined contribution pension plans as well as the rise in LTC expenses—researchers, policymakers, and insurance companies have expressed considerable interest in these products. Despite significant welfare gains in theory, the market for them still remains small today. One potential reason is that available products are priced above the actuarially fair premium. This is particularly true for the LTC insurance market, where markups are significant and have experienced a steep rise in recent years (Ko 2016). In this paper we provide a new explanation for the high loads in the LTC insurance market, which rests on the uncertainty of future longevity and morbidity and on solvency constraints imposed by regulators. We focus on annuiti
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