Discrete approximations of continuous distributions by maximum entropy

In numerically implementing the optimization of an expected value in many economic models, it is often necessary to approximate a given continuous probability distribution by a discrete distribution. We propose an approximation method based on the principle of maximum entropy and minimum Kullback–Leibler information, which is computationally very simple. Our method is not intended to replace existing methods but to complement them by “fine-tuning” probabilities so as to match prescribed (not necessarily polynomial) moments exactly.