Optimal growth strategies for a representative agent in a continuous-time asset market

TL;DR

This paper models a continuous-time asset market with many agents, deriving the optimal investment strategy for market stability and showing that proportional investment based on expected dividends is optimal.

Contribution

It introduces a multi-agent mean-field model and identifies the optimal strategy for market agents to prevent outperformance by individual strategies.

Findings

Optimal strategy involves proportional investment to expected dividend intensities.

Market stability is maintained when agents follow the derived optimal strategy.

The model provides conditions under which individual agents cannot outperform the market.

Abstract

We propose a multi-agent model of an asset market and study conditions that guarantee that the strategy of an individual agent cannot outperform the market. The model assumes a mean-field approximation of the market by considering an infinite number of infinitesimal agents who use the same strategy and another infinitesimal agent with a different strategy who tries to outperform the market. We show that the optimal strategy for the market agents is to split their investment budgets among the assets proportionally to their discounted expected relative dividend intensities.