金融学观点的随机微积分基础ELEMENTARY STOCHASTIC CALCULUS, WITH FINANCE IN VIEW pdf epub azw3 2024 下载

This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance.In particular, the Black-Scholes option pricing formula is derived. Thebook can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants

to learn about It6 calculus and/or stochastic finance.

Reader Guidelines

1 Preliminaries

1.1 Basic Concepts from Probability Theory

1.1.1 Random Variables

1.1.2 Random Vectors

1.1.3 Independence and Dependence

1.2 Stochastic Processes

1.3 Brownian Motion

1.3.1 Defining Properties

1.3.2 Processes Derived from Brownian Motion

1.3.3 Simulation of Brownian Sample Paths

1.4 Conditional Expectation

1.4.1 Conditional Expectation under Discrete Condition .

1.4.2 About a-Fields

1.4.3 The General Conditional Expectation

1.4.4 Rules for the Calculation of Conditional Expectations

1.4.5 The Projection Property of Conditional Expectations

1.5 Martingales

1.5.1 Defining Properties

1.5.2 Examples

1.5.3 Tile Interpretation of a Martingale as a FaiI: Game

2 The Stochastic Integral

2.1 The Riemann and Riemann Stieltjes Integrals

2.1.1 The Ordinary Riemann Integral

2.1.2 The Riemann Stieltjes Integral

2.2 The It6 Integral

2.2.1 A Motivating Example

2.2.2 The It6 Stochastic Integral for Simple Processes

2.2.3 The General It6 Stochastic Integral

2.3 The It6 Lemma

2.3.1 The Classical Chain Rule of Differentiation

2.3.2 A Simple Version of the It6 Lemma

2.3.3 Extended Versions of the It6 Lemma

2.4 The Stratonovich and Other Integrals

3 Stochastic Differential Equations

3.1 Deterministic Differential Equations

3.2 It6 Stochastic Differential Equations

3.2.1 What is a Stochastic Differential Equation?

3.2.2 Solving It6 Stochastic Differential Equations by the It6 Lemma

3.2.3 Solving It6 Differential Equations via Stratonovich Cal-culus

3.3 The General Linear Differential Equation

3.3.1 Linear Equations with Additive Noise

3.3.2 Homogeneous Equations with Multiplicative Noise

3.3.3 The General Case

3.3.4 The Expectation and Variance Functions of the Solution

3.4 Numerical Solution

3.4.1 The Euler Approximation

3.4.2 The Milstein Approximation

4 Applications of Stochastic Calculus in Finance

4.1 The Black-Scholes Option Pricing Formula

4.1.1 A Short Excursion into Finance

4.1.2 What is an Option?

4.1.3 A Mathematical Formulation of the Option Pricing Problem

4.1.4 The Black and Scholes Formula

4.2 A Useful Technique: Change of Measure

4.2.1 What is a Change of tile Underlying Measure?

4.2.2 An Interpretation of the Black-Scholes Formula by Chan-ge of Measure

Appendix

A1 Modes of Convergence

A2 Inequalities

……

Bibliography

Index

List of Abbreviations and Symbols

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书籍介绍

Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This text should be suitable for the reader without a deep mathematical background. It seeks to provide an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived.

• 作者： Tinker 发布时间：2008-10-17 11:17:00

  通俗易懂

• 作者： cheerzzh 发布时间：2014-11-05 20:45:48

  懂了的不用看 不懂的看了也挺迷茫。。

• 作者： 伍赟Allan 发布时间：2012-10-03 12:24:09

  写得还算清楚、简洁。不过貌似泊松过程只提了一下，做题的时候傻眼了...

• 作者： 翁小样 发布时间：2014-11-16 16:14:39

  https://book.douban.com/review/7194525/

• 作者： Renco 发布时间：2013-11-02 07:01:30

  很好的书 可以用来梳理体系

• 作者： 月球漫舞者 发布时间：2010-04-23 23:45:18

  从数学角度来看这本书是一星，给四星是因为能把这么深的数学写成一本那么简单的书，能够让那么多人读懂，也算够强大了。。。

• 一天的书

  作者：混路的阿鹏哥 发布时间：2011-09-29 14:47:25

  搞不清楚作者的定位是哪一类读者，个人感觉是懂得看了觉得太简单，不懂的看了也不太明白讲什么。整本书比较有点意思的地方时插了不少图（也许是我少见多怪），看过的其他随机分析有关的书中，好像没见过有这么多图的。anyway，这是一本一天内可以看完的书，也许对刚接触布朗运动的读者有些用吧，瞎猜的。

• 并没有那么简单

  作者：Raincy 发布时间：2018-06-01 22:41:59

  说简单的人你有仔细推敲并想明白其中的细节吗？还是说囫囵吞枣？

  这本书对于非数专业的高年级本科生也并不那么容易阅读

  在第一章条件期望，sigma代数系统的讲解已经是高等概率论的知识了，虽然作者没有基于测度论来讲解并且尽力诉说着一些“东西”，但是一些概念和定理本身就很抽象，想彻底想通这本书确实很难做到，但是脑子灵活的话应该能灵光一闪大致理解其中意味