Mathematical Finance

  1. Discrete-Time Financial Models
    1. Single-Period Models
      1. One-Period Binomial Model
        1. Model Setup
          1. Asset Price Dynamics
            1. Risk-Free Asset
              1. Market Assumptions
              2. Replicating Portfolios
                1. Portfolio Construction
                  1. Hedging Strategies
                    1. Self-Financing Condition
                    2. Risk-Neutral Pricing
                      1. Risk-Neutral Probability
                        1. Pricing Formula
                          1. Interpretation
                          2. State Prices
                            1. Arrow-Debreu Securities
                              1. Complete Market Pricing
                            2. General Single-Period Model
                              1. Multiple States
                                1. Multiple Assets
                                  1. Arbitrage-Free Pricing
                                    1. Fundamental Theorems
                                  2. Multi-Period Models
                                    1. Multi-Period Binomial Model
                                      1. Binomial Trees
                                        1. Tree Construction
                                          1. Recombining Trees
                                            1. Parameter Selection
                                            2. Dynamic Trading Strategies
                                              1. Self-Financing Strategies
                                                1. Portfolio Rebalancing
                                                  1. Hedging in Multiple Periods
                                                  2. American Option Pricing
                                                    1. Early Exercise Feature
                                                      1. Optimal Exercise Strategy
                                                        1. Backward Induction Algorithm
                                                        2. Convergence Properties
                                                          1. Limiting Behavior
                                                            1. Connection to Continuous Models
                                                          2. General Multi-Period Models
                                                            1. Discrete-Time Market Model
                                                              1. Martingale Measures
                                                                1. Completeness in Multi-Period Setting
                                                                  1. Dynamic Programming Approach

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                                                              2. Probability Theory for Finance

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                                                              4. Stochastic Calculus