Hedging Goals

TL;DR

This paper explores goal-based investing through the lens of option hedging, incorporating risk aversion, and introduces a novel reinforcement learning approach for optimal investment strategies considering transaction costs.

Contribution

It extends the connection between goal-based investing and option hedging by including risk aversion and presents the first model-free reinforcement learning algorithm for optimal goal-based investing with transaction costs.

Findings

Maximizing goal achievement probability and minimizing expected shortfall are equivalent in optimal policies.

Introduces a model-free reinforcement learning method for goal-based investing.

Provides the first algorithmic solution accounting for transaction costs in this context.

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.