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內容簡介

　　We translate to the domain of mathematical finance what F. Knight wrote， in substance， in the preface of his Essentials of Brownian Motion and Diffusion （1981）: "it takes some temerity for the prospective author to embark on yet another discussion of the concepts and main applications of mathematical finance". Yet， this is what we have tried to do in our own way， after considerable hesitation.

內頁插圖

目錄

Part I Continuous Path Processes
1 Continuous-Path R.andom Processes: Mathematical Prerequisites
1.1 Some Definitions
1.1.1 Measurability
1.1.2 Monotone Class Theorem
1.1.3 Probability Measures
1.1.4 Filtration
1.1.5 Law of a Random Variable, Expectation
1.1.6 Independence
1.1.7 Equivalent Probabilities and Radon-Nikodym Densities
1.1.8 Construction of Simple. Probability Spaces
1.1.9 Conditional Expectation
1.1.10 Stochastic Processes
1.1.11 Convergence
1.1.12 Laplace Transform
1.1.13 Gaussian Processes
1.1.14 Markov Processes
1.1.15 Uniform Integrability
1.2 Martingales
1.2.1 Definition and Main Properties
1.2.2 Spaces of Martingales
1.2.3 Stopping Times
1.2.4 Local Martingales
1.3 Continuous Semi-martingales
1.3.1 Brackets of Continuous Local Martingales
1.3.2 Brackets of Continuous Semi-martingales
1.4 Brownian Motion
1.4.1 One-dimensional Brownian Motion
1.4.2 d-dimensional Brownian Motion
1.4.3 Correlated Brownian Motions
1.5 Stochastic Calculus
1.5.1 Stochastic Integration
1.5.2 Integration by Parts
1.5.3 Ito's Formula: The Fu.ndamental Formula of Stochastic Calculus
1.5.4 Stochastic Differential Equations
1.5.5 Stochastic Differential Equations: The One- dimensional Case
1.5.6 Partial Differential Equations
1.5.7 Doleans-Dade Exponential
1.6 Predictable Representation Property
1.6.1 Brownian Motion Case
1.6.2 Towards a General Definition of the Predictable Representation Property
1.6.3 Dudley's Theorem
1.6.4 Backward Stochastic Differential Equations ,
1.7 Change of Probability and Girsanov's Theorem
1.7.1 Change of Probability
1.7.2 Decomposition of IP-Martingales as Q-semi-martingales
1.7.3 Girsanov's Theorem: The One-dimensional Brownian Motion Case
1.7.4 Multidimensional Case
1.7.5 Absolute Continuity
1.7.6 Condition for Martingale Property of Exponential Local Martingales
1.7.7 Predictable Represen tation Property under a Change of Probability
1.7.8 An Example of Invariance of BM under Change of Measure
2 Basic Concepts and Examples in Finance
2.1 A Semi-martingale Framework
2.1.1 The Financial Market
2.1.2 Arbitrage Opportunities
2.1.3 Equivalent Martingale Measure
2.1.4 Admissible Strategies
2.1.5 Complete Market
2.2 A Diffusion Model
2.2.1 Absence of Arbitrage
2.2.2 Completeness of the Market
2.2.3 PDE Evaluation of Contingent Claims in a Complete Market
2.3 The Black and Scholes Model
2.3.1 The Model
……

Part II Jump Processes

Index of Authors
Index of Symbols
Subject Index

前言/序言

金融市場用的數學方法（英文） [Mathematical Methods for Financial Markets] 下載 mobi epub pdf txt 電子書

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