Hi guys,Regarding nonlinear problems, I just wanted to let you know that I recently coauthored the book Nonlinear Option Pricing with Pierre Henry-Labordere: http://www.crcpress.com/product/isbn/9781466570337Quick
overview: Our book covers a wide variety of topics such as American options, uncertain volatility, transaction costs, illiquid markets, super-replication under delta and gamma constraints, uncertain mortality, different rates for borrowing and lending, CVA, smile calibration of local stochastic volatility models, path-dependent volatility models, and local correlation models, etc.The purpose of the book is to present and compare various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. To the best of our knowledge, this is the first monograph dedicated to nonlinear option pricing. We present many different methods in the same book, when usually they are described separately. This allows us to compare their efficiency. Certain methods suggested in this book are original contributions to the field, including regression methods and dual methods for pricing chooser options, the Monte Carlo approaches for pricing in the uncertain lapse and mortality model and in the uncertain volatility model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options, with or without stochastic interest rates, the affine transform technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of solutions of some nonlinear PDEs based on marked branching diffusions.We focus on general mathematical tools rather than on specific financial questions. The main advantage in doing so is that the tools can be straightforwardly used by readers to solve their own (nonlinear) problems. We strove to make the book reasonably comprehensive, and to find a right balance between ideas, mathematical theory, and numerical implementations. We devote ample space to the theory: the relevant mathematical notions are introduced, the important results are given, and some proofs are either detailed or sketched when needed, or when it is instructive. But the main focus is deliberately on ideas and on numerical examples, which we believe help a lot in understanding the tools and building intuition. In this respect, this book is meant to be a practitioner's guide: all the mathematical methods that are introduced are illustrated on practical nonlinear option pricing problems. In layman's terms, these problems have been considered in our careers as quantitative analysts.The table of contents of the book, as well as sample pages, are available at books.google.com/books?isbn=1466570334.I hope this was informative!