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書籍詳細




洋書

数理ファイナンス:問題と解法 第1巻:確率解析

Problems and Solutions in Mathematical Finance : Stochastic Calculus

(The Wiley Finance Series)

Chin, Eric   Nel, Dian   Olafsson, Sverrir

John Wiley & Sons Inc 2014/10
379 p. 26 cm   
装丁: Hrd    装丁について
テキストの言語: ENG    出版国: US
ISBN: 9781119965831
KCN: 1016808008
紀伊國屋書店 選定タイトル
標準価格:¥9,724(本体 ¥8,840)   
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納期について
DDC: 332.0151922
KDC: E210 金融理論
F181 金融数理・金融工学
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Annotation

Volume I provides a comprehensive explanation of stochastic calculus and probability theory focusing on their relationship with mathematical finance.

Full Description

Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance.
Detailed information

Table of Contents

Preface ix Prologue xi About the Authors xv 1 General Probability Theory 1 1.1 Introduction 1 1.2 Problems and Solutions 4 1.2.1 Probability Spaces 4 1.2.2 Discrete and Continuous Random Variables 11 1.2.3 Properties of Expectations 41 2 Wiener Process 51 2.1 Introduction 51 2.2 Problems and Solutions 55 2.2.1 Basic Properties 55 2.2.2 Markov Property 68 2.2.3 Martingale Property 71 2.2.4 First Passage Time 76 2.2.5 Reflection Principle 84 2.2.6 Quadratic Variation 89 3 Stochastic Differential Equations 95 3.1 Introduction 95 3.2 Problems and Solutions 102 3.2.1 It-o Calculus 102 3.2.2 One-Dimensional Diffusion Process 123 3.2.3 Multi-Dimensional Diffusion Process 155 4 Change of Measure 185 4.1 Introduction 185 4.2 Problems and Solutions 192 4.2.1 Martingale Representation Theorem 192 4.2.2 Girsanov s Theorem 194 4.2.3 Risk-Neutral Measure 221 5 Poisson Process 243 5.1 Introduction 243 5.2 Problems and Solutions 251 5.2.1 Properties of Poisson Process 251 5.2.2 Jump Diffusion Process 281 5.2.3 Girsanov s Theorem for Jump Processes 298 5.2.4 Risk-Neutral Measure for Jump Processes 322 Appendix A Mathematics Formulae 331 Appendix B Probability Theory Formulae 341 Appendix C Differential Equations Formulae 357 Bibliography 365 Notation 369 Index 373