Annuitization and asset allocation under exponential utility

作者：Liang, Xiaoqing; Young, Virginia R.^*

来源：Insurance: Mathematics and Economics , 2018, 79: 167-183.

DOI：10.1016/j.insmatheco.2018.01.005

• Life annuities
• Optimal consumption
• Optimal investment
• Stochastic control
• Free-boundary problem

We find the optimal investment, consumption, and annuitization strategies for a retiree who wishes to maximize her expected discounted utility of lifetime consumption. We assume that the retiree's preferences exhibit constant absolute risk aversion (CARA), that is, the retiree's utility function is exponential. The retiree invests in a financial market with one riskless and one risky asset, the so-called Black-Scholes market. Moreover, the retiree may purchase single-premium immediate life annuity income that is payable continuously, and she may purchase this life annuity income at any time and for any amount, subject to the limit of her available wealth.
Because maximizing exponential utility generally does not prevent wealth from dropping below 0, we restrict the investment, consumption, and annuitization strategies so that wealth remains non-negative. We solve the optimization problem via stochastic control and obtain semi-explicit solutions by using the Legendre dual. We prove that the optimal annuitization strategy is a barrier strategy. We also provide some numerical examples to illustrate our results and to analyze their sensitivity to the parameters.

• 出版日期2018-3
• 单位河北工业大学