金融学观点的随机微积分基础ELEMENTARY STOCHASTIC CALCULUS, WITH FINANCE IN VIEW mobi 下载 网盘 caj lrf pdf txt 阿里云

This book is suitable for the reade***ithout a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reade***ith a great deal of measure theory. Applicati*** are taken from stochastic finance.In particular, the Black-Sc***s 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 Expectati***

1.4.5 The Projection Property of Conditional Expectati***

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 Versi*** of the It6 Lemma

2.4 The Stratonovich and Other Integrals

3 Stochastic Differential Equati***

3.1 Deterministic Differential Equati***

3.2 It6 Stochastic Differential Equati***

3.2.1 What is a Stochastic Differential Equation?

3.2.2 Solving It6 Stochastic Differential Equati*** by the It6 Lemma

3.2.3 Solving It6 Differential Equati*** via Stratonovich Cal-culus

3.3 The General Linear Differential Equation

3.3.1 Linear Equati*** with Additive Noise

3.3.2 Homogeneous Equati*** with Multiplicative Noise

3.3.3 The General Case

3.3.4 The Expectation and Variance Functi*** of the Solution

3.4 Numerical Solution

3.4.1 The Euler Approximation

3.4.2 The Milstein Approximation

4 Applicati*** of Stochastic Calculus in Finance

4.1 The Black-Sc***s 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 Sc***s Formula

4.2 ***seful Technique: Change of Measure

4.2.1 What is a Change of tile Underlying Measure?

4.2.2 An Interpretation of the Black-Sc***s Formula by Chan-ge of Measure

Appendix

A1 Modes of Convergence

A2 Inequalities

……

Bibliography

Index

List of Abbreviati*** and Symbols

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书籍介绍

Modelling with the Ito integral or stochastic differential equati*** 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 reade***ithout a deep mathematical background. It seeks to provide an elementary introduction to that area of probability theory, without burdening the reade***ith a great deal of measure theory. Applicati*** are taken from stochastic finance. In particular, the Black-Sc***s option pricing formula is derived.