Data-driven distributionally robust Kelly portfolio optimization based on coherent Wasserstein metrics

The Kelly strategy is a common approach in portfolio optimization problems that aims to maximize the expected portfolio growth rate in the long term. Its computation requires complete knowledge of the asset return distribution, which is obviously not observable, but can be inferred from sample data. Motivated by recent developments in data-driven optimization methods, we propose a new class of coherent Wasserstein data-driven Kelly portfolio optimization models. In particular, we establish a class of ambiguity sets based on coherent Wasserstein metrics, and these new metrics can strike a good balance between robustness and data-drivenness, thus providing richer choices for ambiguity set design. The Kelly portfolio optimization model, which is data-driven and based on coherent Wasserstein balls, can be solved efficiently as a finite-dimensional convex program. This model also provides a robust data-driven solution. In addition, we numerically investigate the proposed model and find that it outperforms the type-1 Wasserstein–Kelly portfolio, especially the classical Kelly portfolio. Moreover, it indicates that we can obtain a portfolio with higher final value and stability, especially in controlling volatility and maximum drawdown.