Annuities, long-term care insurance, and insurer solvency

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.