Fundamentals and Advanced Techniques in Derivatives Hedging
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.
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absence of arbitrage American option arbitrage arbitrage opportunities arguments assume Black and Scholes bounded Brownian motion characterisation complete markets compute consider continuous convergence convex Deduce defined definition delta-hedging denote density derivative dynamic programming principle equation equivalent European option Exercise exists formula given hedging price hedging strategy implies inequality Itô's lemma Lipschitz local volatility M.QS Malliavin derivative market is complete martingale measure martingale representation theorem maturity measure Q Moreover obtain optimal option of payoff payoff G polynomial growth portfolio constraints predictable process probability measure Proposition Q-martingale random variable resp risk neutral risk neutral measure risk-free interest rate risky asset satisfies Scholes model Sect Show stochastic volatility sub-solution super-hedging price super-replication price super-solution supermartingale Theorem 1.4 unique viable price viscosity solution wealth process Zºº