1 Department of Management Engineering, Technical University of Denmark2 Management Science, Department of Management Engineering, Technical University of Denmark
We optimize the asset allocation, consumption and bequest decisions of an investor with uncertain lifetime and under time-varying investment opportunities. The asset menu is given by stocks, zero coupon bonds and pure endowments with dierent maturities. The latter are contingent on either a single or a joint life, and pay xed or variable benets. We further include transaction costs on stocks and bonds, and surrender charges on pure endowments. We show that despite high surrender charges, annuities are the primary asset class in a portfolio, and that annuity income is never fully consumed, but used for rebalancing purposes. We argue that the optimal retirement product for a household is much more complex than any of those available in the market. Every household should be oered an annuity tailored to its needs, using a unique combination of assets and mortality protection levels.