This book directly focuses on finding optimal trading strategies in the real world and supports that with a well-defined theoretical foundation that allows trading strategy problems to be solved. Critically, it also delivers a menu of actual solutions that can be applied by traders with various risk profiles and objectives in markets that exhibit substantial tail risk. It shows how the Markowitz approach leads to excessive risk taking, and trader underperformance, in the real world. It summarizes the key features of Utility Theory, the deficiencies of the Sharpe Ratio as a statistic, and develops an optimal decision theory with fully developed examples for both 'Normal' and leptokurtotic distributions.