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Beschreibung
This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to… continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts ofthe square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
21.10.2021
Sprache
Englisch
EAN
9789811588662
Herausgeber
Springer Singapore
Serien- oder Bandtitel
Monographs in Mathematical Economics
Sonderedition
Nein
Autor
Shigeo Kusuoka
Seitenanzahl
218
Einbandart
Broschiert
Autorenporträt
The author is currently Professor Emeritus at The University of Tokyo and visiting Professor at Meiji University. He previously held positions at The University of Tokyo and Research Institute for Mathematical Sciences, Kyoto University. He was an invited speaker at the ICM 1990.
Schlagwörter
Martingale for Continuous Time Parameters, Stochastic Integrals, Brownian Motions, Stochastic Differential Equations, Euler--Maruyama Approximations, Applications to Mathematical Finances
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PBKL - Integralrechnung und -gleichungen
PBKF - Funktionalanalysis und Abwandlungen
PBW - Angewandte Mathematik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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