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Book Review

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Book Information:

Title: Stochastic calculus for finance
Additional book information: Springer Finance Textbook Series, in two volumes, Vol. I: The binomial asset pricing model, Steven E. Shreve, Springer, New York, 2005, x + 187 pages, ISBN 978-0387-24968-1, $34.95; 2004, x + 550 pages, ISBN 0-387-40101-6, $69.95

References [Enhancements On Off] (What's this?)

  • 1. Bachelier, L. (1900).
    Théorie de la Speculation.
    Annales Scientifiques de L'École Normale Supérieure 3d ser., 17, 21-88. Translation in The Random Character of Stock Market Prices, ed. Paul Cootner, pp. 17-79. Cambridge, MA: MIT Press, 1964.
  • 2. Black, F. and M. Scholes (1973).
    The Pricing of Options and Corporate Liabilities.
    Journal of Political Economy 81, 637-654.
  • 3. Cox, J., J. Ingersoll, and S. Ross (1985).
    A Theory of the Term Structure of Interest Rates.
    Econometrica 53, 385-408. MR 785475
  • 4. Cox, J. and S. Ross (1976).
    The Valuation of Options for Alternative Stochastic Processes.
    Journal of Financial Economics 3, 145-166.
  • 5. Cox, J., S. Ross, and M. Rubinstein (1979).
    Option Pricing: A Simplified Approach.
    Journal of Financial Economics 7, 229-263.
  • 6. Delbaen, F. and W. Schachermayer (1999).
    A General Version of the Fundamental Theorem of Asset Pricing.
    Mathematische Annalen 300, 463-520. MR 1304434 (95m:90022b)
  • 7. Doeblin, V. (1940).
    Sur l'Equation de Kolmogorov.
    Comptes Rendus de L'Académie de Sciences, Ser. I 331, 1059-1102.
  • 8. Einstein, A. (1905).
    Uber die von der Molekularkinetischen Theorie der Wärme gefordete Bewegung von in ruhenden Flüssigkeiten suspendieren Teilchen.
    Annalen der Physik und Chemie 17, 549-560, Reprinted as ``On the Movement of Small Particles Suspended in Static Liquids as Claimed in the Molecular Kinetic Theory of Heat'' in Investigations of the Theory of Brownian Movement, ed. R. Fürth, New York: Dover, 1956.
  • 9. Ethier, S. and T. Kurtz (1986).
    Markov Processes: Characterization and Convergence.
    New York: Wiley. MR 838085 (88a:60130)
  • 10. Harrison, M. and D. Kreps (1979).
    Martingales and Arbitrage in Multiperiod Securities Markets.
    Journal of Economic Theory 20, 381-408. MR 540823 (80h:90025)
  • 11. Harrison, M. and S. Pliska (1981).
    Martingales and Stochastic Integrals in the Theory of Continuous Trading.
    Stochastic Processes and Their Applications 11, 215-260. MR 622165 (83a:90022)
  • 12. Itô, K. (1944).
    Stochastic Integral.
    Proceedings of the Imperial Academy of Tokyo 20, 519-524. MR 0014633 (7:313c)
  • 13. Itô, K. (1951).
    On a Formula Concerning Stochastic Differentials.
    Nagoya Mathematics Journal 3, 55-65. MR 0044063 (13:363g)
  • 14. Jarrow, R. and P. Protter (2004).
    A Short History of Stochastic Integration and Mathematical Finance: The Early Years, 1880-1970.
    Herman Rubin Festschrift, IMA Lecture Notes 45, 75-91. MR 2126888 (2006a:60005)
  • 15. Karatzas, I. and S. Shreve (1998).
    Methods of Mathematical Finance.
    New York: Springer-Verlag. MR 1640352 (2000e:91076)
  • 16. Merton, R. (1969).
    Lifetime Portfolio Selection under Uncertainty: The Continuous Time Case.
    Review of Economics and Statistics 51, 247-257.
  • 17. Merton, R. (1973).
    The Theory of Rational Option Pricing.
    Bell Journal of Economics and Management Science 4, 141-183. MR 0496534 (58:15058)
  • 18. Protter, P. (2001).
    A Partial Introduction to Finance.
    Stochastic Processes and Their Applications 91(2), 169-203. MR 1807684 (2001k:91082)
  • 19. Protter, P. (2004).
    Stochastic Integration and Differential Equations, Second Edition.
    New York: Springer-Verlag. MR 2020294 (2005k:60008)
  • 20. Samuelson, P. (1965a).
    Proof that Properly Anticipated Prices Fluctuate Randomly.
    Industrial Management Review 6, 41-49.
  • 21. Samuelson, P. (1965b).
    Rational Theory of Warrant Pricing.
    Industrial Management Review 6, 13-39.
  • 22. Shreve, S. (2004).
    Stochastic Calculus for Finance II: Continuous-Time Models.
    New York: Springer. MR 2057928 (2005c:91001)
  • 23. Shreve, S. (2005).
    Stochastic Calculus for Finance I: The Binomial Asset-Pricing Model.
    New York: Springer. MR 2049045 (2004m:91003)
  • 24. Vasicek, O. (1977).
    An Equilibrium Characterization of the Term Structure.
    Journal of Financial Economics 5, 177-188.
  • 25. Wiener, N. (1923).
    Differential Space.
    Journal of Mathematical Physics 2, 131-174.

Review Information:

Reviewer: Darrell Duffie
Affiliation: Graduate School of Business, Stanford University, Stanford, California 94305-5015
Journal: Bull. Amer. Math. Soc. 46 (2009), 165-174
MSC (2000): Primary 60-01, 60H10, 60J65, 91B28.
DOI: https://doi.org/10.1090/S0273-0979-08-01217-2
Published electronically: August 28, 2008
Additional Notes: I am grateful for conversations with Julien Hugonnier and Philip Protter, for decades worth of interesting discussions with Mike Harrison, and also for the patient encouragement of the editor, Bob Devaney.
Review copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society