Essentials of Stochastic Finance: Facts, Models, Theory
This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks.
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Chapter II Stochastic Models Discrete Time
Chapter III Stochastic Models Continuous Time
Chapter IV Statistical Analysis of Financial Data
Part 2 THEORY
Chapter V Theory of Arbitrage in Stochastic Financial Models Discrete Time
Chapter VI Theory of Pricing in Stochastic Financial Models Discrete Time
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1-measurable absence of arbitrage American options analysis arbitrage arbitrage-free arbitrage-free market asset assume assumption asymptotic arbitrage bank account Black–Scholes call option Chapter condition consider corresponding decomposition defined definition density distribution equation equivalent example exists filtered probability space financial mathematics finite formula Girsanov's theorem hedging Hence independent interest rate lemma LÚvy process local martingale Markov martingale measure martingale with respect means obtain optimal stopping P-martingale parameter pay-off function portfolio predictable probabilistic probability measure problem proof put option random variables rational price relation representation result S)-market satisfies self-financing semimartingale sequence h solution space Q standard statistical stochastic differential stochastic differential equation stochastic integral strategy supermartingale theorem theory volatility Wiener process