About this book
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.
While there are many books on the financial mathematics of incomplete markets based on probability, and equivalent martingale measure approach to pricing, this book is based solely on the analytical aspects of stochastic control, or more precisely, portfolio optimization. Namely, relying solely on portfolio optimization, neutral and indifference pricing as well as hedging methodologies were fully developed in the context of arbitrary diffusive Markovian market models and portfolios of contracts. That was made possible by some recent discoveries, the most specific one being a recently found matrix inverse – the fundamental matrix of derivatives pricing and hedging.
This approach, while very general, is very feasible for practical implementations. So, many examples are fully derived. The reader will get the full understanding of the relationship between neutral and indifference pricing, how to implement either one of these pricing methodologies, how to implement hedging methodologies, and how to apply all these in equity portfolio valuations and foreign exchange.
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).