203372618 Pliska Introduction to Mathematical Finance

Introduction to Mathematical Finance
Discrete Time Models

Stanley R. Pliska

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Contents
Preface

iii

Acknowledgments
1

2

viii

Single Period Securities Markets
1.1 Model Specifications . . . . . . . . . . . . .
1.2 Arbitrage and other Economic Considerations
1.3 Risk Neutral Probability Measures . . . . . .
1.4 Valuation of Contingent Claims . . . . . . . .
1.5 Complete and Incomplete Markets . . . . . .
1.6 Risk and Return . . . . . . . . . . . . . . . .

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Single Period Consumption and Investment
2.1 Optimal Portfolios and Viability . . . . . . . . . . . . . 2.2 Risk Neutral Computational Approach . . . . . . . . . .
2.3 Consumption Investment Problems . . . . . . . . . . . .
2.4 Mean-Variance Portfolio Analysis . . . . . . . . . . . . 2.5 Portfolio Management with Short Sales Restrictions and
straints . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Optimal Portfolios in Incomplete Markets . . . . . . . . 2.7 Equilibrium Models . . . . . . . . . . . . . . . . . . . .

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Similar Con. . . . . . . .
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3 Multiperiod Securities Markets
3.1 Model Specifications, Filtrations, and Stochastic Processes 3.1.1 Information Structures . . . . . . . . . . . . . . .
3.1.2 Stochastic Process Models of Security Prices . . .
3.1.3 Trading Strategies . . . . . . . . . . . . . . . . .
3.1.4 Value Processes and Gains Processes . . . . . . .
3.2 Self-Financing Trading Strategies . . . . . . . . . . . . . 3.2.1 Discounted Prices . . . . . . . . . . . . . . . . . .
3.3 Return and Dividend Processes . . . . . . . . . . . . . . . 3.3.1 Returns for Discounted Price Processes . . . . . .
3.3.2 Returns for the Value and Gains Processes . . . . .
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CONTENTS

ii

3.4
3.5
3.6

3.3.3 Dividend Processes . . . . . . . .
Conditional Expectation and Martingales
Economic Considerations . . . . . . . . .
Markov Models . . . . . . . . . . . . . .

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4 Options, Futures, and Other Derivatives
4.1 Contingent Claims . . . . . . . . . . . . . .
4.2 European Options Under the Binomial Model
4.3 American Options . . . . . . . . . . . . . . .
4.4 Complete and Incomplete Markets . . . . . .
4.5 Forward Prices and Cash Stream Valuation . .
4.6 Futures . . . . . . . . . . . . . . . . . . . .

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