Valuation of derivatives: from fundamental theorems to risk-constrained hedging.

Summary This book provides a comprehensive overview of the mathematical fundamentals of financial asset pricing and derivative hedging. The abstract theory of asset pricing is presented in detail in a general framework of discrete-time models before being extended to continuous-time models. It then presents in depth the hedging techniques applied in Markovian models: in complete market, in incomplete market or in the presence of portfolio constraints. The study relies heavily on the characterization of prices as solutions of partial differential equations in the classical sense or in the sense of viscosity solutions. The originality of this book also lies in the presentation of recent stochastic target techniques that allow the study of non-classical models (such as those used in high frequency trading) and the calculation of prices defined according to a risk criterion. Essential practical notions such as calibration, the impact of a model specification error or the ability to set up a dynamic hedge are also discussed. Each chapter is completed with a series of exercises and examples corresponding to industry standards.