Introduction to Mathematical Finance: Discrete Time Models

Model Specifications.

Arbitrage and Other Economic Consideration.

Risk Neutral Probability Measures.

Valuation of Contingent Claims.

Complete and Incomplete Markets.

Risk and Return.

Part II: Single Period Consumption and Investment:.

Optimal Portfolios and Viability.

Risk Neutral Computational Approach.

Consumption Investment Problems.

Mean-Variance Portfolio Analysis.

Portfolio Management with Short Sales Constraints and Similar Restrictions.

Optimal Portfolios in Incomplete Markets.

Equilibrium Models.

Part III: Multiperiod Securities Markets:.

Model Specifications, Filtrations, and Stochastic Processes.

Information Structures.

Stochastic Process Models of Security Prices.

Trading Strategies.

Value Processes and Gains Processes.

Self-Financing Trading Strategies.

Discounted Prices.

Return and Dividend Processes.

Conditional Expectation and Martingales.

Economic Considerations.

The Binomial Model.

Markov Models.

Part IV: Options, Futures, and Other Derivatives:.

Contingent Claims.

European Options Under the Binomial Model.

American Options.

Complete and Incomplete Markets.

Forward Prices and Cash Stream Valuation.

Futures.

Part V: Optimal Consumption and Investment Problems:.

Optimal Portfolios and Dynamic Programming.

Optimal Portfolios and Martingals Methods.

Consumption-Investment and Dynamic Programming.

Consumption-Investment and Martingale Methods.

Maximum Utility from Consumption and Terminal Wealth.

Optimal Portfolios with Constraints.

Optimal Consumption-Investment with Constraints.

Portfolio Optimization in Incomplete Markets.

Part VI: Bonds and Interest Rate Derivatives:.

The Basic Term Structure Model.

Lattice, Markov Chain Models.

Yield Curve Models.

Forward Risk Adjusted Probability Measures.

Coupon Bonds and Bond Options.

Swaps and Swaptions.

Caps and Floors.

Part VII: Models with Infinite Sample Spaces.

Finite Horizon Models.

Infinite Horizon Models.