1 Foundation of Probability Theory and Discrete-Time Martingales
1.1 Basic Concepts of Probability Theory
1.1.1 Events and Probability
1.1.2 Independence, 0-1 Law, and Borel-Cantelli Lemma
1.1.3 Integrals, (Mathematical) Expectations of Random Variables
1.1.4 Convergence Theorems
1.2 Conditional Mathematical Expectation
1.2.1 Definition and Basic Properties
1.2.2 Convergence Theorems
1.2.3 Two Theorems About Conditional Expectation
1.3 Duals of Spaces L∞(Ω, F) and L∞(Ω, F, m)
1.4 Family of Uniformly Integrable Random Variables
1.5 Discrete Time Martingales
1.5.1 Basic Definitions
1.5.2 Basic Theorems
1.5.3 Martingale Transforms
1.5.4 Snell Envelop
1.6 Markoy Sequences
2 Portfolio Selection Theory in Discrete.Time
2.1 Mean-Variance Analysis
2.1.1 Mean-Variance Frontier Portfolios Without Risk-Free Asset
2.1.2 Revised Formulations of Mean-Variance Analysis Without Risk-Free Asset
2.1.3 Mean-Variance Frontier Portfolios with Risk-Free Asset
2.1.4 Mean-Variance Utility Functions
2.2 Capital Asset Pricing Model (CAPM)
2.2.1 Market Competitive Equilibrium and Market Portfolio.,
2.2.2 CAPM with Risk-Free Asset
2.2.3 CAPM Without Risk-Free Asset
2.2.4 Equilibrium Pricing Using CAPM
2.3 Arbitrage Pricing Theory (APT)
2.4 Mean-Sernivariance Model
2.5 Multistage Mean-Variance Model
2.6 Expected Utility Theory
2.6.1 Utility Functions
2.6.2 Arrow-Pratt's Risk Aversion Functions
2.6.3 Comparison of Risk Aversion Functions
2.6.4 Preference Defined by Stochastic Orders
2.6.5 Maximization of Expected Utility and Initial Price of Risky Asset
2.7 Consumption-Based Asset Pricing Models
3 Financial Markets in Discrete Time
3.1 Basic Concepts of Financial Markets
3.1.1 Numeraire
3.1.2 Pricing and Hedging
3.1.3 Put-Call Parity
3.1.4 Intrinsic Value and Time Value
3.1.5 Bid-Ask Spread
3.1.6 Efficient Market Hypothesis
3.2 Binomial Tree Model
3.2.1 The One-Period Case
3.2.2 The Multistage Case
3.2.3 The Approximately Continuous Trading Case
3.3 The General Discrete-Time Model
3.3.1 The Basic Framework
3.3.2 Arbitrage, Admissible, and Allowable Strategies
3.4 Martingale Characterization of No-Arbitrage Markets
3.4.1 The Finite Market Case
3.4.2 The General Case: Dalang-Morton-Willinger Theorem..
3.5 Pricing of European Contingent Claims
3.6 Maximization of Expected Utility and Option Pricing
3.6.1 General Utility Function Case
3.6.2 HARA Utility Functions and Their Duality Case
3.6.3 Utility Function-Based Pricing
3.6.4 Market Equilibrium Pricing
3.7 American Contingent Claims Pricing
3.7.1 Super-Hedging Strategies in Complete Markets
3.7.2 Arbitrage-Free Pricing in Complete Markets
3.7.3 Arbitrage-Free Pricing in Non-complete Markets
4 Martingale Theory and It8 Stochastic Analysis
4.1 Continuous Time Stochastic Processes
4.1.1 Basic Concepts of Stochastic Processes
4.1.2 Poisson and Compound Poisson Processes
4.1.3 Markov Processes
4.1.4 Brownian Motion
4.1.5 Stopping Times, Martingales, Local Martingales
4.1.6 Finite Variation Processes
4.1.7 Doob-Meyer Decomposition of Local Submartingales
4.1.8 Quadratic Variation Processes of Semimartingales
4.2 Stochastic Integrals w.t.t. Brownian Motion
4.2.1 Wiener Integrals
4.2.2 Ito Stochastic Integrals
4.3 Itr's Formula and Girsanov's Theorem
4.3.1 Itr's Formula
4.3.2 Lrvy's Martingale Characterization of Brownian Motion
4.3.3 Reflection Principle of Brownian Motion
4.3.4 Stochastic Exponentials and Novikov Theorem
4.3.5 Girsanov's Theorem
4.4 Martingale Representation Theorem
4.5 Ito Stochastic Differential Equations
4.5.1 Existence and Uni

严加安著的《随机金融引论(英文版)(精)》系统地介绍了金融数学的基本理论——ICS，重点介绍了鞅方法在未定权益定价和套期保值中的应用、利率期限结构模型和期望效用最大化问题。本文还给出了半鞅模型的n个市场以及金融市场的无数值、原始概率框架，给出了概率的基本理论和伊藤的随机分析理论，作为初步知识。