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$59.95$
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, DOI 10.1111/1467-9965.t01-1-00003
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, DOI 10.1515/9783110858389
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, DOI 10.1007/PL00013529
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, DOI 10.1007/s007800050068
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, DOI 10.1111/1467-9965.00011
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.
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 (English, with English and French summaries). MR 1990027, DOI 10.1016/S1631-073X(03)00189-4
D. Nualart and É. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (1988), no. 4, 535–581. MR 950346, DOI 10.1007/BF00353876
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, DOI 10.1080/17442509108833682
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, DOI 10.1007/BFb0084154
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; by Springer-Verlag, Berlin, 1984. Notes by M. Gopalan Nair and B. Rajeev. MR 742628
Shinzo Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), no. 1, 1–39. MR 877589
- 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
- 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
- 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
- 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
- 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
- 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
- 8.
- D. Nualart and É. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (1988), no. 4, 535-581. MR 0950346
- 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 0742628
- 12.
- Shinzo Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), no. 1, 1-39. MR 0877589
Review Information:
Reviewer:
David Nualart
Affiliation:
Kansas University
Email:
nualart@math.ku.edu
Journal:
Bull. Amer. Math. Soc.
44 (2007), 487-492
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.
