关键词: 老龄化风险, 老龄化债券, 固定缴款养老金, 随机最优控制, HJB 方程

Abstract: Longevity risk has attracted increasing attention in financial mathematics and financial engineering area. Longevity bond is defined as a kind of financial instrument to hedge longevity risk. To investigate whether the longevity bond can hedge longevity risk in defined contribution (DC) pension plans effectively, this paper deals with two optimal management problems for a DC pension plan during its accumulation phase and decumulation phase, respectively. For both problems, the scheme aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal fund by investing its wealth in a financial market consisting of a longevity bond and a risk-free asset. Closed-form optimal investment strategies are derived by using the dynamic programming approach and solving the related HJB equation. Under rational assumptions, the results reveal that the maximal expected utility under the market with a longevity bond is higher than the maximal expected utility under the market with an ordinary bond, in both phases.

Key words: longevity risk, longevity bond, DC pension plan, stochastic optimal control, HJB equation