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 [Bro99b] 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. [FL99]) and minimizing the expected shortfall (efficient hedging, cf. [FL00]) 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.
Keywords
Cite
@article{arxiv.2105.07915,
title = {Hedging Goals},
author = {Thomas Krabichler and Marcus Wunsch},
journal= {arXiv preprint arXiv:2105.07915},
year = {2021}
}