Risk-Adjusted Kelly Investing Under Non-Homogeneous Reward and Risk

In financial applications, the Kelly criterion is a well-known strategy for maximizing long-term growth, but is often criticized for its high-risk approach. To mitigate this effect, previous research proposed two risk-adjusted Kelly criteria in a finite investment horizon: the inflection point, which identifies optimal marginal return, and the optimal reward-to-risk ratio. These approaches maintain the core benefits of the Kelly criterion while reducing risk. As the investment size is used as a proxy for risk, the theory is developed under a linear and smooth setting. However, in practical cases such as transaction costs, reward and risk become non-homogeneous and non-smooth, thus requiring the development of a novel non-smooth analysis framework for risk-adjusted Kelly strategies, which we conduct in this paper. After developing the theory, we apply it to several practical settings, and extend the framework to multiple assets. The research concludes with an empirical analysis of the risk and reward of the risk-adjusted Kelly strategies applied to transaction costs, confirming the superiority of the proposed strategies to the classical Kelly criterion.