Book excerpt: This book is written for quantitative finance professionals, students, educators, and mathematically inclined individual investors. It is about some of the latest developments in pricing, hedging, and investing in incomplete markets. With regard to pricing, two frameworks are fully elaborated: neutral and indifference pricing. With regard to hedging, the most conservative and relaxed hedging formulas are derived. With regard to investing, the neutral pricing methodology is also considered as a tool for connecting market asset prices with optimal positions in such assets. Srdjan D. Stojanovic is Professor in the Department of Mathematical Sciences at University of Cincinnati (USA) and Professor in the Center for Financial Engineering at Suzhou University (China).