203372618 Pliska Introduction to Mathematical Finance

Topics: Probability theory, Linear programming, Random variable Pages: 522 (101767 words) Published: May 4, 2015
Introduction to Mathematical Finance
Discrete Time Models

Stanley R. Pliska

2

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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Bibliography: 1. Bartle, Robert G. and Sherbert, Donald R. 1992: Introduction to Real Analysis, Wiley,
New York.
3. Bazaraa, M. S. 1993: Nonlinear Programming, Wiley, New York.
4. Berberian, Sterling K. 1994: A First Course in Real Analysis, Spnnger-Verlag, New York.
5. Bertsekas, Dmiitri P. 1976: Dynamic Programming and Stochastic Control, Academic
Press, New York.
8. Browder, Andrew, Halmos, P. R. and Axler, S. 1996: Mathematical Analysis: An Introduction, Springer Verlag, New York.
9. Brown, William C. 1991: Matrices and Vector Spaces, Marcel Dekker, New York.
10. Chiang, Alpha C. 1974: Fundamental Methods of Mathematical Economics, McGraw
Hill, New York.
11. Chvatal, V. 1980: Linear Programming. W.H. Freeman & Co., New York.
12. Cinlar, Erhan, 1975: Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs,
NJ.
14. Dalang, R., Morton, A. and Willinger, W., 1990: “Equivalent martingale measures and
no-arbitrage in stochastic securities market models”, Stochastics and Stochastic Reports,
15. Dantzig, G. B. 1998: Linear Programming and Extensions, Princeton University Press,
Princeton, NJ.
16. Denardo, Eric V. 1982: Dynamic Programming: Models and Applications, PrenticeHall,
Englewood Cliffs, NJ.
17. Dixit, Avinash K. 1990: Optimization in Economic Theory, Oxford University Press, Oxford.
18. Dixit, Avinash K. and Pindyck, Robert S. 1994: Investment Under Uncertainty, Princeton
University Press, Princeton, NJ.
19. Doob, J. L. 1953: Stochastic Processes, Wiley, New York.
20. Dothan, Michael U. 1990: Prices in Financial Markets, Oxford University Press, Oxford.
28. Gantmacher. F R. 1959: The Theory of Matrices, 2 vols, Chelsea, New York.
29. Harrison, J. Michael and Pliska. Stanley, R. 1981: “Martingales and stochastic integrals
in the theory of continuous trading,” Stochastic Processes and Their Applications, 11, pp.
31. Hoel, P., Port, S. and Stone. C. 1972: Introduction to Stochastic Processes, Houghton
Muffin, Boston.
32. Huang, Chi-fu and Litzenberger, Robert H. 1988: Foundations for Financial Economics,
North-Holland, New York.
34. Ingersoll, Jr., Jonathan E. 1987: Theory of Financial Decision Making, Rowman & Littlefield, Totowa, NJ.
35. Jarrow, Robert A. 1988: Finance Theory, Prentice-Flail, Englewood Cliffs, NJ.
37. Jeter. Melvyn W. 1986: Mathematical Programming: An Introduction to Optimization.
38. Karatzas, loannis and Shreve, Steven E. 1998: Methods of Mathematical Finance, SpringerVerlag, New York.
39. Karlin, Samuel and Taylor, Howard M. 1975: A First Course in Stochastic Processes,
Academic Press, New York.
41. Karr, Alan F. 1993: Probability, Springer-Verlag, New York.
43. Klein, E. 1973: Mathematical Methods in Theoretical Economics, Academic Press, New
York.
47. Luenberger, David G. 1998: Investment Science, Oxford University Press, Oxford.
49. Merton, Robert C. 1990: Continuous-Time Finance, Blackwell, Oxford.
52. Murty, Katta G. 1976: Linear and Combinatorial Programming, Wiley, New York.
54. Neveu, J. 1975: Discrete-parameter Martingales, North-Holland, Amsterdam.
55. Norris, J. 1998: Markov Chains, Cambridge University Press, Cambridge.
58. Panjer. Harry et al. 1998: Financial Economics, With Applications to Investments, Insurance and Pensions, The Actuarial Foundation, Schaumburg, Illinois.
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