To extend this framework to settings with more than two investment options or with a continuous state space, the model would need to be adapted to accommodate the increased complexity. In the case of more than two investment options, the optimal strategy would involve evaluating the potential returns and risks associated with each option and determining the optimal allocation of funds among the available choices.
In settings with a continuous state space, the model would need to incorporate a broader range of possible states and information sources. This could involve using techniques from stochastic calculus or machine learning to analyze and make decisions based on continuous data streams. The optimal strategy would involve dynamically updating the decision-making process based on real-time information and adjusting the investment portfolio to maximize returns and minimize risks in a continuously changing environment.