Reinforcement Learning Approaches for Optimal Exploration in Incomplete Markets

In this article, we explore the concept of reinforcement learning (RL) and its application to the famous Merton problem in finance. RL is a powerful tool for solving complex problems by learning from experience. In the context of Merton’s problem, RL can help find optimal strategies for investing in an incomplete market, where some information about the underlying assets is missing.
To understand how RL works, let’s first consider a simple example. Imagine you are trying to learn how to play a game by trial and error. You start with a basic policy (i.e., strategy) and then experiment with different actions. Based on the rewards or punishments you receive, you update your policy to improve its performance. This process continues until you reach a level of optimization.
Now, let’s apply this idea to Merton’s problem. In this scenario, we want to find the best strategy for investing in an incomplete market. We start by randomly selecting a policy and then observing the rewards or punishments associated with each action. Using these observations, we update our policy to improve its performance. This process continues until we reach an optimal solution.
The key insight here is that RL allows us to balance exploration (trying new things) and exploitation (sticking with what works). By iteratively updating our policy based on the rewards or punishments we receive, we can avoid getting stuck in a suboptimal strategy.
One challenge in applying RL to Merton’s problem is dealing with the inherent complexity of financial markets. Unlike games, where the rules are clear-cut and predictable, financial markets are subject to various factors that can impact investment decisions. To overcome this hurdle, we use a technique called "stochastic policy gradient methods," which allows us to learn from simulated data.
Another important consideration is the issue of overfitting, where the algorithm becomes too specialized to the training data and fails to generalize well to new situations. To address this problem, we propose a "recursive weighting scheme" that helps maintain a balance between exploration and exploitation.
In summary, RL offers a powerful approach for solving Merton’s problem in an incomplete market. By iteratively updating policies based on rewards or punishments, we can find optimal strategies that balance exploration and exploitation. While there are challenges to overcome, the potential benefits of using RL in finance make it an exciting area of research with significant practical implications.