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Additional Readings

1   Preliminaries and Review

• Inverse Matrices and Solving Linear Systems of Equations
• Proving the Fundamental Theorem of Calculus

2   Probability and Risk

• A Verification of the Central Limit Theorem

3   Discrete Time and State Models

    Nothing yet

4    Continuous Time and State Models

    Nothing yet

5   An Introduction to Stochastic Processes and Applications

• Verifying the Martingale Property for Subsequent Periods
• Brownian Motion as a Limit of a Discrete Random Walk
• Geometric Brownian Motion as a Limit of a Discrete Stochastic Process
• Verification of the Tower Property

6   Introduction to Stochastic Calculus

• Doob Decomposition
• Verification of the Itô Isometry

7   Derivatives Pricing and Applications of Stochastic Calculus

• Solving the Black-Scholes Differential Equation
• More on the Self-Financing Replicating Portfolio and the Black-Scholes Derivation
• Deriving Black-Scholes Delta and Gamma

8   Mean-Reverting Processes and Term Structure Modeling

• Deriving the PDE Solution for Pricing a Long-Term Bond
• Additional Applications for Mean Reverting Processes

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