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Mathematical Finance

Mathematical Finance

Wydawnictwo Springer Nature Switzerland AG
Data wydania 21/12/2020
Liczba stron 772
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
ISBN 9783030261085
Kategorie Finanse i rachunkowość, Finanse, Zarządzanie i style zarządzania, Prawdopodobieństwo i statystyka, Matematyka stosowana
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Opis książki

Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Mathematical Finance

Spis treści

Part I.- Stochastic Calculus.- Overview.- Discrete Stochastic Calculus.- Levy Processes.- Stochastic Integration.- Semimartingale Characteristics.- Markov Processes.- Affine and Polynomial Processes.- Optimal Control.- Mathematical Finance.- Overview and Notation.- Equity models.- Markets, Strategies, Arbitrage.- Optimal Investment.- Arbitrage-Based Valuation and Hedging of Derivatives.- Mean-Variance Hedging.- Utility-Based Valuation and Hedging of Derivatives.- Interest Rate Models.

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