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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 Theoremout 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

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