✍ Scribed by Bruno Bouchard, Jean-François Chassagneux (auth.)
No coin nor oath required. For personal study only.
This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A large spectrum of concepts and mathematical tools that are usually found in separate monographs are presented here. In addition to the no-arbitrage theory in full generality, this book also explores models and practical hedging and pricing issues. Fundamentals and Advanced Techniques in Derivatives Hedging further introduces advanced methods in probability and analysis, including Malliavin calculus and the theory of viscosity solutions, as well as the recent theory of stochastic targets and its use in risk management, making it the first textbook covering this topic.
Graduate students in applied mathematics with an understanding of probability theory and stochastic calculus will find this book useful to gain a deeper understanding of fundamental concepts and methods in mathematical finance.
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Discrete Time Models....Pages 3-53
Continuous Time Models....Pages 55-106
Optimal Management and Price Selection....Pages 107-124
Front Matter....Pages 125-125
Delta Hedging in Complete Market....Pages 127-165
Super-Replication and Its Practical Limits....Pages 167-191
Hedging Under Loss Constraints....Pages 193-224
Front Matter....Pages 225-225
Local Volatility Models....Pages 227-254
Stochastic Volatility Models....Pages 255-272
Back Matter....Pages 273-280
Quantitative Finance; Probability Theory and Stochastic Processes; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization
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