Optimal portfolio choice in jump-diffusion markets with longevity risk

In the present paper, we provide the solution to an optimal portfolio choice problem for an investment strategy endowed with a specific class of investment mechanism, the so called Target-Date funds. The proposal must ensure a minimum level of gain from the investment at maturity and hypothesizes uncertainty in the interest rate, contribution rate, and mortality. In addition, the financial setting assumes the presence of discontinuities in the dynamics of risky assets to reflect the occurrence of market crashes. To hedge against investment, longevity, and event risks, we complete the market using a zero-coupon bond, a longevity zero-coupon bond, and a derivative, respectively. We apply standard dynamic programming techniques and obtain closed-form solutions to the stochastic control problem with the objective of maximizing the expected utility of terminal cushion. We complete the picture by performing an extensive numerical analysis on real data, to measure the impact of market crashes and the effect of hedging tools.