An Annuitization Problem in the Tax-Deferred Annuity Model

This paper examines the optimal annuitization, investment, and consumption strategies of an individual facing a time-dependent mortality rate in the tax-deferred annuity model and considers both the case when the rate of buying annuities is unrestricted and the case when it is restricted. At the beginning, by using the dynamic programming principle, we obtain the corresponding HJB equation. Since the existence of the tax and the time-dependence of the value function make the corresponding HJB equation hard to solve, firstly, we analyze the problem in a simpler case and use some numerical methods to get the solution and some of its useful properties. Then, by using the obtained properties and Kuhn–Tucker conditions, we discuss the problem in general cases and get the value functions and the optimal annuitization strategies, respectively.

Interaction effects between dynamic hybrid products and traditional deferred annuities in the German life insurance market

Dynamic hybrid products emerged in 2007 and are now well established in the German life insurance market. In this article, we study interaction effects between dynamic hybrid products and traditional deferred annuity contracts, that are sold by the same insurance company. The key question we investigate is whether the presence of dynamic hybrid products has a negative effect on the payout of traditional insurance products. We do so by using data drawn from a Monte Carlo simulation that is based on a model presented in this article. These data reveal that dynamic hybrid products reduce the payment to policyholders of traditional deferred annuities via the channel of surplus participation.

Addressing Longevity Risk: How Best to Annuitize Defined Contribution Assets?

Unlike defined benefit pensions, 401(k) plans provide little guidance on how to turn accumulated assets into income. The key risk that retirees face is outliving their assets. Insurance against such risk is available through several routes, including immediate annuities, deferred annuities, and additional Social Security through delayed claiming. Under this Social Security bridge option, participants would tap their 401(k) for payments equal to their Social Security to delay claiming. This paper compares these three options in simulations against a baseline in which no assets are used to obtain lifetime income. In each option, assets not allocated to purchasing lifetime income are consumed following the Required Minimum Distribution rules. The analysis finds that, when market and health shocks are included alongside longevity uncertainty, the Social Security bridge option is generally the best for households with median wealth. Wealthier households can benefit from combining the bridge option with a deferred annuity. Part of a symposium sponsored by the Economics of Aging Interest Group.

Cumulative prospect theory and deferred annuities

Purpose Although it has been proved theoretically that annuities can provide optimal consumption during one’s retirement period, retirees’ reluctance to purchase annuities is a long-standing puzzle. The purpose of this paper is to use behavioral model to analyze the low demand for immediate annuities. Design/methodology/approach The authors employ cumulative prospect theory (CPT), which contains both loss aversion and probability transformations, to analyze the annuity puzzle. Findings The authors show that CPT can explain the unattractiveness of immediate annuities. It also shows that retirees would be willing to buy a long-term deferred annuity at retirement. By considering each component from CPT in turn, the loss aversion is found to be the major reason that stops people from buying an annuity while the survival rate transformation is an important factor affecting the decision of when to receive annuity incomes. Originality/value This paper identifies CPT as one of the reasons for the low demand of immediate annuities. It further suggests that long-term deferred annuities could overcome behavioral obstacles and become popular among retirees.

Demographic risk in deep-deferred annuity valuation

A deep-deferred annuity is a deferred annuity where payments start very late in life, i.e. well after the normal retirement age. This annuity has received much attention lately as it was made accessible to 401(k) plans in the United States in 2014. By transferring the risk of outliving retirement savings at high ages to annuity providers, deep-deferred annuities provide annuitants with enhanced later-life financial security. However, the valuation of this annuity suffers from high uncertainty because the mortality data at high ages are sparse and possibly unreliable. In this paper, we use risk ratio to measure demographic risk in the valuation. Demographic risk is decomposed into the following four components: (1) mortality tail curve risk, (2) mortality improvement model risk, (3) parameter risk in mortality tail curves, and (4) parameter risk in mortality improvement rate models. Our quantitative analysis aims to provide insights into the development and risk management of deep-deferred annuities.