Asymmetric information propagation frequently results in distorted financial markets and is generally a feature of informationally inefficient markets. We developed a model of optimal asset allocation using the martingale method to assist an investor in selecting an asset that performs better under the conditions of a market information cascade. In order to confirm that the model satisfies the required conditions, we applied the verification theorem and ascertained that the results produced were optimal. The model outperformed the famous Markowitz mean-variance type model and was shown to produce stable and consistent solutions under such market conditions.