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Book Review

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Book Information:

Authors: Paul Malliavin and Anton Thalmaier
Title: Stochastic calculus of variations in mathematical finance
Additional book information: Springer-Verlag, Berlin, 2006, xii+142 pp., ISBN 978-3-540-43431-3, US$59.95

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

  • 1. Emilio Barucci, Paul Malliavin, Maria Elvira Mancino, Roberto Renò, and Anton Thalmaier, The price-volatility feedback rate: an implementable mathematical indicator of market stability, Math. Finance 13 (2003), no. 1, 17-35, Conference on Applications of Malliavin Calculus in Finance (Rocquencourt, 2001). MR 1968094 (2004d:91099)
  • 2. Nicolas Bouleau and Francis Hirsch, Dirichlet forms and analysis on Wiener space, de Gruyter Studies in Mathematics, vol. 14, Walter de Gruyter & Co., Berlin, 1991. MR 1133391 (93e:60107)
  • 3. Eric Fournié, Jean-Michel Lasry, Jérôme Lebuchoux, and Pierre-Louis Lions, Applications of Malliavin calculus to Monte-Carlo methods in finance. II, Finance Stoch. 5 (2001), no. 2, 201-236. MR 1841717 (2002e:91063)
  • 4. Eric Fournié, Jean-Michel Lasry, Jérôme Lebuchoux, Pierre-Louis Lions, and Nizar Touzi, Applications of Malliavin calculus to Monte Carlo methods in finance, Finance Stoch. 3 (1999), no. 4, 391-412. MR 1842285 (2002e:91062)
  • 5. Peter Imkeller, Malliavin's calculus in insider models: additional utility and free lunches, Math. Finance 13 (2003), no. 1, 153-169, Conference on Applications of Malliavin Calculus in Finance (Rocquencourt, 2001). MR 1968102 (2004b:91079)
  • 6. Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) (New York-Chichester-Brisbane), Wiley, 1978, pp. 195-263.
  • 7. Paul Malliavin and Anton Thalmaier, Numerical error for SDE: asymptotic expansion and hyperdistributions, C. R. Math. Acad. Sci. Paris 336 (2003), no. 10, 851-856. MR 1990027 (2004d:60142)
  • 8. D. Nualart and É. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (1988), no. 4, 535-581. MR 950346 (89h:60089)
  • 9. Daniel L. Ocone and Ioannis Karatzas, A generalized Clark representation formula, with application to optimal portfolios, Stochastics Stochastics Rep. 34 (1991), no. 3-4, 187-220. MR 1124835 (93b:60098)
  • 10. Gilles Pisier, Riesz transforms: a simpler analytic proof of P.-A. Meyer's inequality, Séminaire de Probabilités, XXII, Lecture Notes in Math., vol. 1321, Springer, Berlin, 1988, pp. 485-501. MR 960544 (89m:60178)
  • 11. S. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 73, published for the Tata Institute of Fundamental Research, Bombay, 1984; notes by M. Gopalan Nair and B. Rajeev. MR 742628 (86b:60113)
  • 12. Shinzo Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), no. 1, 1-39. MR 877589 (88h:60111)

Review Information:

Reviewer: David Nualart
Affiliation: Kansas University
Email: nualart@math.ku.edu
Journal: Bull. Amer. Math. Soc. 44 (2007), 487-492
MSC (2000): Primary 60H07, 60H30; Secondary 91B24
Published electronically: April 10, 2007
Review copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society