Default Risk of Life Annuity and the Annuity Puzzle

Abstract

This paper considers a model of optimal consumption and portfolio choice of the retired person who has partially annuitized her wealth and faces default risk of her annuity provider. We develop a new method for solving the optimal consumption and portfolio choice problem in an incomplete financial market. We find that the effects of default risk on the retiree's optimal investment strategies and annuity demand depend crucially on the level of default risk, risk aversion, wealth, and investment opportunity. Higher default risk may lead retired people to increase their stock holdings. Lower default risk can substantially increase the demand for annuities. The annuity demand increases as risk aversion increases if default risk is small, whereas the annuity demand decreases as risk aversion increases if default risk is large.