stochastic-calculus

KO | EN

gitlite — search

#javascript #python #llm #golang #machine-learning #deep-learning #docker #nodejs #java #vue #security #pytorch #openai #open-source

stochastic-calculus

(★ 65)

Stochastic calculus handbook pdf

stochastic-calculus 최신버젼 다운로드

최종 버전 다운로드 (.zip)

// repository documentation

Was this content helpful?

★ 0 (0 ratings)

# 《Stochastic Calculus》中英文自学笔记

![version](https://img.shields.io/badge/version-1.0-blue)
![Status](https://img.shields.io/badge/Status-building-brightgreen)
![PRs Welcome](https://img.shields.io/badge/PRs-welcome-brightgreen.svg)
![stars](https://img.shields.io/github/stars/PlusYoung/stochastic-calculus)
![Fork](https://img.shields.io/github/forks/PlusYoung/stochastic-calculus)
![Issues](https://img.shields.io/github/issues/PlusYoung/stochastic-calculus)

## 项目动机

随机分析是金融工程专业的高级课程，是通往衍生品定价和做Q-quant的必学之课。它复杂又严谨，但对于没有学过测度论、高等概率论和实变函数的同学，在初步学习随机分析的过程中可能会非常受挫。这里，第一章的内容将带大家预习/复习一些随机分析将用到的一些高等概率论和实变函数的知识。这些知识可以应付60%的后续随机分析的内容，如果你是高等概率论和实分析小白，没有听过σ-代数和Borel集，那么第一章将作为扫盲章，为你后续的学习起到非常巨大的承接作用！后面所有的章节都由浅入深，层层递进，欢迎大家阅读指正！

如果你是Q-quant爱好者，并致力于深入学习衍生品定价的理论，我推荐Claudio Landim的B站Measure Theory和Probability Theory这两门课程，它们将带你搭建整套测度论和高等概率论知识体系！

**本项目的特色：**

- 笔记内容深入浅出，覆盖随机分析的基本概念和应用。
- 利用图解和实例使得复杂的概念变得容易理解。
- 提供一份系统的学习指南，以帮助学习者更有效地掌握随机分析。

本项目所用徽章来自互联网，如侵犯了您的图片版权请联系我们删除，谢谢。并且由于我们的水平有限，有任何问题和错误请批评指正，谢谢。

## 课程简介

随机分析结合了概率论和微积分，主要研究随机过程的微分性质。它在金融工程中的应用尤为广泛，特别是在期权定价和风险管理中。本教程介绍随机分析的基本概念，包括布朗运动、随机积分、伊藤引理、以及随机微分方程。本教程适合具备一定数学背景的学习者，特别是对金融数学和随机过程感兴趣的人。

## 课程资源

- 推荐书籍：Steven Shreve - "Stochastic Calculus for Finance"
- 推荐视频：Coursera - "Stochastic Processes and Models"

## 笔记

### Chapter 1: Basics
- [1-1: Probability Space](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter1.pdf)
- [1-2: Random Variables](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter1.pdf)
- [1-3: Expectations](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter1.pdf)

### Chapter 2: Advanced Topics
- [2-1: Conditional Probability and Conditional Expectation](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter2-1.pdf)
- [2-2: Discrete Time Martingales](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter2-2.pdf)
- [2-3: Martingale Transform and Doob Decompesition](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter2-3.pdf)

### Chapter 3: One Period Model

- [3-1: Portfolios](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-1-2.pdf)
- [3-2: Derivative Securities](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-1-2.pdf)
- [3-3: Absence of Arbitrage](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-3-4.pdf)
- [3-4: No Arbitrage and Price System](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-3-4.pdf)
- [3-5: Martingale Measures](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-5.pdf)
- [3-6: Pricing](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-6.pdf)
- [3-7: Complete Market Model](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter3-7.pdf)

### Chapter 4: Multi Period Model
- [4-1: The Market Model](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter4-1.pdf)
- [4-2: Arbitrage Opportunity](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter4-2.pdf)
- [4-3: Martingale Measures](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter4-3.pdf)
- [4-4: Aribitrage-free Prices for European Contingent Claim](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter4-4.pdf)

### Chapter 5: Stopping Time
- [5-1: The Stopping Time](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter5-1.pdf)
- [5-2: American Claims](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter5-2.pdf)
- [5-3: Arbitrage-free Prices](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter5-3.pdf)

### Chapter 6: Measures of Risk
- [6-0: Measures of Risk](https://github.com/PlusYoung/stochastic-calculus/blob/main/chapter6-0.pdf)

stochastic-calculus

stochastic-calculus 최신버젼 다운로드

오늘의 추천 프로젝트

Was this content helpful?

Recent Feedback

stochastic-calculus

stochastic-calculus 최신버젼 다운로드

오늘의 추천 프로젝트

Was this content helpful?

Recent Feedback

Download README