Almost all relevant decisions have attached values or outcomes that are uncertain. However, when a complete description of the uncertainties is unknown, traditional models struggle to provide an optimal course of action. In this book, I present a modeling procedure to analyze stochastic decisions with underspecified joint probability distributions. The book is directed to researchers and practitioners with the interest of modeling problems where the structure of the uncertainties is partially known. This work represents a four-fold project. First, a new framework for joint probability distribution approximations is provided. Second, a new joint distribution simulation procedure (JDSIM) is developed. JDSIM sample joint probability distributions from the set of all possible distributions that match the available information. Third, a framework for testing the accuracy of different joint probability distribution approximations is developed. Finally, a new approach to decision making under uncertainty is proposed. The techniques in this book will provide the reader with the tools to model and analyze decisions with a new and deeper understanding of the relevant uncertainties.