Hedging goals

Abstract

Goal-based investing is concerned with reaching a monetary investment goal by a given finite deadline, which differs from mean-variance optimization in modern portfolio theory. In this article, we expand the close connection between goal-based investing and option hedging that was originally discovered in Browne (Adv Appl Probab 31(2):551–577, 1999) by allowing for varying degrees of investor risk aversion using lower partial moments of different orders. Moreover, we show that maximizing the probability of reaching the goal (quantile hedging, cf. Föllmer and Leukert in Finance Stoch 3:251–273, 1999) and minimizing the expected shortfall (efficient hedging, cf. Föllmer and Leukert in Finance Stoch 4:117–146, 2000) yield, in fact, the same optimal investment policy. We furthermore present an innovative and model-free approach to goal-based investing using methods of reinforcement learning. To the best of our knowledge, we offer the first algorithmic approach to goal-based investing that can find optimal solutions in the presence of transaction costs.