Discrete approximations of continuous distributions by maximum entropy

摘要

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 Kull-back-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.