## Essentials of Stochastic Finance: Facts, Models, TheoryThis 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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### Contents

Chapter II Stochastic Models Discrete Time | 80 |

Chapter III Stochastic Models Continuous Time | 188 |

Chapter IV Statistical Analysis of Financial Data | 314 |

Part 2 THEORY | 381 |

Chapter V Theory of Arbitrage in Stochastic Financial Models Discrete Time | 382 |

Chapter VI Theory of Pricing in Stochastic Financial Models Discrete Time | 502 |

Chapter VII Theory of Arbitrage in Stochastic Financial Models Continuous Time | 632 |

Chapter VIII Theory of Pricing in Stochastic Financial Models Continuous Time | 734 |

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### Other editions - View all

Essentials of Stochastic Finance: Facts, Models, Theory Albert N. Shiryaev No preview available - 1999 |

### Common terms and phrases

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 Lévy 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