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 interest rate, contribution rate, and mortality. Moreover, the financial setting assumes the presence of discontinuities in the risky asset dynamics to reflect the occurrence of market crashes. To hedge against investment, longevity and event risks, we complete the market by 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 wealth. 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.

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SHORT BIO: Immacolata Oliva is Associate Professor at Sapienza University of Rome. She received her Ph.D. degree in Mathematics from University of Bologna in 2012, defending a thesis on some algebraic techniques applied to Levy processes theory. She was Post-Doc fellow at several Italian Universities, and visiting researcher at LMU Universitaet in Munich. She is currently teaching Financial Mathematics in the third year of the Bachelor’s degree programme in Economics and Finance, as well as Quantitative Finance and Methods and Models for Finance for the Master’s degree programme in Finance and Insurance. Her research activity spans several areas of Mathematical Finance, including: optimal portfolio allocation problems in continuous-time  models, possibly including the presence of discontinuities; Portfolio Insurance strategies and related derivative pricing; counterparty credit risk management (via BSDEs); numerical approaches to integral equations applied to Finance and Insurance.