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Introduction to Mathematical Finance: Discrete Time Models



Introduction to Mathematical Finance: Discrete Time Models

Stanley R. Pliska

ISBN: 978-1-557-86945-6 July 1997 276 Pages

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The purpose of this book is to provide a rigorous yet accessible introduction to the modern financial theory of security markets. The main subjects are derivatives and portfolio management. The book is intended to be used as a text by advanced undergraduates and beginning graduate students. It is also likely to be useful to practicing financial engineers, portfolio manager, and actuaries who wish to acquire a fundamental understanding of financial theory. The book makes heavy use of mathematics, but not at an advanced level. Various mathematical concepts are developed as needed, and computational examples are emphasized.
Part I: Single Period Securities Markets:.

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.


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.

"I believe that this is an excellent text for undergraduate or MBA classes on Mathematical Finance. The bulk of the book describes a model with finitely many, discrete trading dates, and a finite sample space, thus it avoids the technical difficulties associated with continuous time models. The major strength of this book is its careful balance of mathematical rigor and intuition." Peter Lakner, New York University
* Provides a rigorous treatment of financial theory in a casual style
* Emphasizes computational examples
* Introduces Financial engineering
* Provides accessible introduction to financial models