# 203372618 Pliska Introduction to Mathematical Finance

**Topics:**Probability theory, Linear programming, Random variable

**Pages:**522 (101767 words)

**Published:**May 4, 2015

Discrete Time Models

Stanley R. Pliska

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Contents

Preface

iii

Acknowledgments

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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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