Peter K Friz - Publications
Below a list of paper published until 2009; from 2010 on please click on the link above.
Papers in journals, refereed
conference proceedings
1. with J.C.Robinson: Smooth attractors have zero thickness Mathematical Analysis and Applications 240 (1999)
37-46
2. with J.C.Robinson: Parametrising the
attractor of the 2D Navier-Stokes equation with a
finite set of nodal values, Physica
D148 (2001) 201-220
3. with I. Kukavica & J.C.Robinson:
Nodal parametrisation of analytic attractors;
Discrete and Continuous Dynamical Systems 7
(2001) 643-657
4. with J.C.Robinson: Constructing an elementary measure on a space
of projections; Mathematical Analaysis and
Applications 267 (2002) 714-725
5. with M.Avellaneda, D.Boyer-Olson, J.Busca: Reconstruction of Volatility: Pricing index
options using the steepest-descent approximation, RISK (2003), 91-95,
selected for publication in Exotic Options: The Cutting-edge Collection
Technical Papers Published in Risk 1999-2003
6. with M.Avellaneda, D.Boyer-Olson, J.Busca: Application of large deviation methods to the
pricing of index options in finance, C. R. Math. Acad. Sci.
Paris 336 no 3 (2003) 263-266
7. Continuity of the Ito-map
for Hoelder rough paths with applications to the
support theorem in Hoelder norm, Probability and
Partial Differential Equations in Modern Applied Mathematics, IMA Volumes in
Mathematics and its Applications, Vol 140 (2005)
117-135
7. with N. Victoir: Approximations of the Brownian rough path with
applications to stochastic analysis, Annales de l'Institut Henri Poincare (B)Probability
and Statistics, Vol 41 Issue 4 (2005) 703-724. (Ranked #6 in Top
25 Articles of Annales de l'IHP.)
8. with T. Lyons, D. Stroock: Levy's area under conditioning, Annales de l'Institut Henri
Poincare (B) Probability and Statistics, Vol 42,
Issue 1 (2006) 89-101, (Ranked #7 in Top
25 Articles of Annales de l'IHP.)
9. with J. Gatheral: Pricing volatility derivatives as inverse problem,
Quantitative Finance, Vol 5 Nr 6 (2005) 531-542
10. with N. Victoir: A note on the notion of geometric rough path,
Probability Theory and Related Fields, Vol 136 Nr 3
(2006) 395-416
11. with N. Victoir: A Variation Embedding Theorem and Applications,
Journal of Functional Analysis, Vol 239 Nr 2 (2006)
631-637 (Ranked #15 in Top
25 Articles of JFA.)
12. with L. Coutin, N. Victoir: Good
approximations to rough paths and applications to anticipating stochastic calculus, Annals of Probability 2007,
Vol. 35, No. 3, 1172-1193
13. with N. Victoir: Large Deviation Principle for Enhanced Gaussian
Processes, Annales de l'Institut
Henri Poincare (B) Probability and Statistics, Volume 43, Issue 6,
November-December 2007, Pages 775-785
14. with N. Victoir: The Burkholder-Davis-Gundy Inequality for Enhanced
Martingales, Séminaire de Probabilités
XLI, Donati-Martin, C.; Émery,
M.; Rouault, A.; Stricker, C. (Eds.), Lecture Notes
in Mathematics, Vol. 1934, 2008.
15. with N. Victoir: Euler Estimates for Rough Differential Equations,
Journal of Differential Equations, Vol 244, Issue 2
(2008) 388-412
16. with N. Victoir: Uniformly Subelliptic
Operators and Stochastic Area, Probability Theory and Related Fields, Vol 142 Nr 3-4 (2008) 475-523
17. with T. Cass and N. Victoir: Non-degeneracy of Wiener functionals
arising from rough differential equations, Transactions of the American Math.
Society, 361 (2009), 3359-3371
18. with S. Benaim: Regular Variation and Smile Asymptotics,
Math. Finance Vol. 19 no 1. (2009), 1-12
19. with S. Benaim: Smile Asymptotics II:
Models with Known MGF, J. Appl. Probab.
Volume 45, Number 1 (2008), 16-32
20. with S. Benaim, R. Lee: The Black Scholes Implied Volatility at Extreme Strikes, Chapter 2 in Frontiers in Quant. Finance: Volatility and Credit Risk Modeling, Wiley (2008) PDF
21. with T. Cass:
Densities for Rough Differential Equations under Hoermander's
Condition, Annals of Mathematics, 2010 issue (Volume 171, no. 3).
22. with
M. Caruana, Partial differential equations
driven by rough paths, Journal of Differential Equations, Volume 247, Issue 1, 1 July 2009, Pages 140-173
23. with
H. Oberhauser, Rough path limits of Wong-Zakai type with modified drift term, Journal of Functional
Analysis 256 (2009), pp. 3236-3256
24. with E. Breuillard, M. Huesmann: From
random walks to rough paths, Proc. Amer. Math. Soc. 137 (2009), 3487-3496
Papers in journals, refereed
conference proceedings
Cass, Thomas; Friz, Peter: Densities for Rough Differential Equations under Hoermander's Condition, Annals of Mathematics, May 2010 issue (Volume 171, no. 3). ISSN 0003-486X
Friz, Peter; Victoir, Nicolas: Differential Equations Driven by Gaussian Signals, Annales de l'Institut Henri Poincare (B) Probability and Statistics, May 2010, Vol. 46, No. 2, 369–413. ISSN 0246-0203
Friz, Peter: Implied Volatility: Large Strike Asymptotics in Encyclopedia of Quantitative Finance (February 2010) Cont R. (Ed.) John Wiley & Sons Ltd. Chichester UK. pp. 909-913. ISBN: 978-0-470-05756-8 PDF
Friz, Peter; Keller-Ressel, Martin: Moment Explosions in Encyclopedia of Quantitative Finance (February 2010) Cont R. (Ed.) John Wiley & Sons Ltd. Chichester UK. pp. 1247-1253. ISBN: 978-0-470-05756-8 PDF
Caruana, Michael; Friz, Peter; Oberhauser Harald: A (rough) pathwise approach to a class of nonlinear SPDEs, Annales de l'Institut Henri Poincare (C) Non Linear Analysis (accepted February 2010) ISSN: 0294-1449
Friz, Peter; Oberhauser, Harald: A generalized Fernique theorem and applications, Proc. Amer. Math. Soc. (accepted April 2010). ISSN 0002-9939
Book
Friz, Peter; Victoir, Nicolas: Multidimensional Stochastic
Processes as Rough Paths. Theory and Applications
Cambridge Studies of Advanced Mathematics Vol. 120, 670 p., Cambridge University
Press, March 2010. ISBN: 0521876079
Various (old) lecture notes
Heat Kernels, Parabolic PDEs and Diffusion Processes pdf
An Introduction to Malliavin Calculus pdf
