Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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. John C. Cox, Jonathan E. Ingersoll Jr., and Stephen A. Ross, A theory of the term structure of interest rates, Econometrica 53 (1985), no. 2, 385–407. 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. W. Schachermayer, Martingale measures for discrete-time processes with infinite horizon, Math. Finance 4 (1994), no. 1, 25–55. MR 1286705,
    Freddy Delbaen and Walter Schachermayer, A general version of the fundamental theorem of asset pricing, Math. Ann. 300 (1994), no. 3, 463–520. MR 1304434,
  • 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. Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085
  • 10. J. Michael Harrison and David M. Kreps, Martingales and arbitrage in multiperiod securities markets, J. Econom. Theory 20 (1979), no. 3, 381–408. MR 540823,
  • 11. J. Michael Harrison and Stanley R. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl. 11 (1981), no. 3, 215–260. MR 622165,
  • 12. Kiyosi Itô, Stochastic integral, Proc. Imp. Acad. Tokyo 20 (1944), 519–524. MR 0014633
  • 13. Kiyosi Itô, On a formula concerning stochastic differentials, Nagoya Math. J. 3 (1951), 55–65. MR 0044063
  • 14. Robert Jarrow and Philip Protter, A short history of stochastic integration and mathematical finance: the early years, 1880–1970, A festschrift for Herman Rubin, IMS Lecture Notes Monogr. Ser., vol. 45, Inst. Math. Statist., Beachwood, OH, 2004, pp. 75–91. MR 2126888,
  • 15. Ioannis Karatzas and Steven E. Shreve, Methods of mathematical finance, Applications of Mathematics (New York), vol. 39, Springer-Verlag, New York, 1998. MR 1640352
  • 16. Merton, R. (1969).
    Lifetime Portfolio Selection under Uncertainty: The Continuous Time Case.
    Review of Economics and Statistics 51, 247-257.
  • 17. Robert C. Merton, Theory of rational option pricing, Bell J. Econom. and Management Sci. 4 (1973), 141–183. MR 0496534
  • 18. Philip Protter, A partial introduction to financial asset pricing theory, Stochastic Process. Appl. 91 (2001), no. 2, 169–203. MR 1807684,
  • 19. Philip E. Protter, Stochastic integration and differential equations, 2nd ed., Applications of Mathematics (New York), vol. 21, Springer-Verlag, Berlin, 2004. Stochastic Modelling and Applied Probability. MR 2020294
  • 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. Steven E. Shreve, Stochastic calculus for finance. II, Springer Finance, Springer-Verlag, New York, 2004. Continuous-time models. MR 2057928
  • 23. Steven E. Shreve, Stochastic calculus for finance. I, Springer Finance, Springer-Verlag, New York, 2004. The binomial asset pricing model. MR 2049045
  • 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
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.