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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) Expectati*** 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 Definiti***

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 Formulati*** 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 Functi***

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 Functi***

2.6.2 Arrow-Pratt's Risk Aversion Functi***

2.6.3 Comparison of Risk Aversion Functi***

2.*** Preference Defined by Stochastic Orders

2.6.5 Maximization of Expected Utility and Initial Price of Risky Asset

2.7 C***umption-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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