Inria / Raweb 2006
Presentation of the Team Mathfi

Bibliography

Major publications by the team in recent years

[1]: M. Akian, A. Sulem, M. Taksar.
Dynamic optimisation of long term growth rate for a portfolio with transaction costs - The logarithmic utility case, in: Mathematical Finance, Avril 2001, vol. 11, n^o 2, p. 153–188.
[2]: B. Arouna.
Adaptative Monte Carlo Method, A Variance Reduction technique, in: Monte Carlo Methods and Applications, 2004, vol. 10, n^o 1.
[3]: V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria, Rocquencourt, February 2003, n^o 4718
http://hal.inria.fr/inria-00071868.
[4]: V. Bally, G. Pagès, J. Printems.
First order schemes in the numerical quantization method, in: Mathematical Finance, 2003, vol. 13, n^o 1, p. 1–16.
[5]: E. Clément, D. Lamberton, P. Protter.
An analysis of a least squares regression method for american option pricing, in: Finance and Stochastics, 2002, vol. 6, p. 449–471.
[6]: B. Jourdain, C. Martini.
American prices embedded in European prices, in: Annales de l'IHP, analyse non linéaire, 2001, vol. 18, n^o 1, p. 1-17.
[7]: D. Lamberton, B. Lapeyre.
Une introduction au calcul stochastique appliqué à la finance, traduction anglaise: An introduction to stochastic calculus applied to finance, Chapman and Hall, 1996, Collection Mathématiques et Applications, Ellipses, 1992.
[8]: B. Lapeyre, E. Temam.
Competitive Monte-Carlo Methods for the Pricing of Asian Options, in: Journal of Computational Finance, 2001, vol. 5, n^o 1, p. 39-57.
[9]: D. Lefèvre.
An introduction to Utility Maximization with Partial Observation, in: Finance, 2002, vol. 23
http://hal.inria.fr/inria-00072440.
[10]: B. Øksendal, A. Sulem.
Optimal Consumption and Portfolio with both fixed and proportional transaction costs, in: SIAM J. Control and Optim, 2002, vol. 40, n^o 6, p. 1765–1790.

Publications of the year

Books and Monographs

[11]: B. Øksendal, A. Sulem.
Applied Stochastic Control of Jump Diffusions, Universitext, (260 pages), Second Edition, Springer Verlag, Berlin, Heidelberg, New York, 2007.

Articles in refereed journals and book chapters

[12]: V. Bally.
Lower bounds for the density of a locally elliptic Ito process, in: Annals of Probability, to appear.
[13]: V. Bally, M. Bavouzet, M. Messaoud.
Computations of Gereks using Malliavin Calculus in jump type market models, in: Annals of Applied Probabilites, to appear.
[14]: V. Bally, L. Caramellino, A. Zanette.
A mixed PDE - Monte Carlo approach for pricing credit default index swaptions, in: Decision in Economics and Finance, 2006, vol. 29.
[15]: J.-P. Chancelier, M. Messaoud, A. Sulem.
A policy iteration algorithm for fixed point problems with nonexpansive operators, in: Mathematical Methods of Operations Research, 2006
http://dx.doi.org/10.1007/s00186-006-0103-3.
[16]: E. Clément, D. Lamberton, A. Kohatsu-Higa.
A duality approach for the weak approximation of stochastic differential equations, in: Annals of Applied Probability, August 2006, vol. 16, n^o 3, p. 1124-1154.
[17]: E. Gobet, G. Pagès, H. Pham, J. Printems.
Discretization and simulation for a class of SPDE's with applications to Zakai and McKean-Vlasov equations, in: SIAM J. on Numerical Analysis, to appear.
[18]: S. Graf, H. Luschgy, G. Pagès.
Distortion mismatch in the quantization of probability measures, in: ESAIM PS, To appear.
[19]: S. Graf, H. Luschgy, G. Pagès.
Optimal quantizers for Radon random vectors in a Banach space, in: J. of Approximation, to appear.
[20]: D. Hernandez-Hernandez, A. Schied.
A control approach to robust utility maximization with logarithmic utility and time-consistent penalties, in: Stochastic Processes their Applications, Special volume on Risk Measures, to appear, vol. 24, p. 109-125.
[21]: D. Hernandez-Hernandez, A. Schied.
Robust utility maximization in a stochastic factor model, in: Statistics and Decisions, Special volume on Risk Measures, 2006, vol. 24, p. 109-125.
[22]: T. Klein, Y. Ma, N. Privault.
Convex concentration inequalities and forward-backward stochastic calculus, in: Electronic Journal of Probability, 2006, vol. 11, p. 486-512.
[23]: A. Kohatsu-Higa, A. Sulem.
Utility maximization in an insider influenced market, in: Mathematical Finance, 2006, vol. 16, n^o 1, p. 153–179.
[24]: H. Luschgy, G. Pagès.
Functional quantization of 1-dimensional Brownian diffusions, in: Stochastic Processes and their Applications, 2006, vol. 116, n^o 2, p. 310–336.
[25]: M. N'zi, Y. Ouknine, A. Sulem.
Regularity and representation of viscosity solutions of Partial differential equations via backward stochastic differential equations, in: Stochastic processes and their applications, 2006, vol. 116, n^o 9, p. 1319–1339.
[26]: N. Privault, A. Réveillac.
Superefficient drift estimation on the Wiener space, in: C. R. Acad. Sci. Paris, 2006, vol. 343, p. 607-612.

Publications in Conferences and Workshops

[27]: A. Joulin, N. Privault.
A logarithmic Sobolev inequality for an interacting spin system under a geometric reference measure, in: Quantum Probability and White Noise Analysis, World Scientific, Proceedings of the 2005 Levico conference, 2006, vol. XX.
[28]: A. Kohatsu-Higa, A. Sulem.
A large trader-insider model, in: Stochastic Processes and Applications to Mathematical Finance, J. Akahori, S. Ogawa, S. Watanabe (editors), World Scientific, Proceedings Ritsumeikan International Symposium, Japan, March 2005, 2006, p. 101-124.
[29]: J.-A. López-Mimbela, N. Privault.
Critical exponents for semilinear PDEs with bounded potentials, Progress in Probability, Birkhäuser, Proceedings of the seminar on stochastic analysis, random fields and applications, Ascona, 2005, To Appear.
[30]: Y. Ma, N. Privault.
FKG inequality on the Wiener space via predictable representation.

Internal Reports

[31]: A. Alfonsi, B. Jourdain.
A Call-Put Duality for Perpetual American Options, Preprint, CREMICS/ENPC, 2006, n^o 307.
[32]: D. David, N. Privault.
Numerical computation of Theta in a jump-diffusion model by integration by parts, Technical report, INRIA, 2006, n^o 32
http://hal.inria.fr/inria-00070196.
[33]: M. Gaudenzi, M. Lepellere, A. Zanette.
The Singular Points Binomial Method for pricing American path-dependent options, Working paper, Dipartimento di Finanza dell'impresa e dei Mercati Finanziari Universita' di Udine, 2006.
[34]: B. Jourdain.
Stochastic flows approach to Dupire's formula, Preprint, CREMICS/ENPC, 2006, n^o 326.
[35]: J. Lelong, C. Labart.
Pricing double barrier Parisian Options using Laplace transforms, Preprint, CREMICS/ENPC, 2006, n^o 328
http://cermics.enpc.fr/reports/CERMICS-2006/CERMICS-2006-328.pdf.
[36]: J. Lelong.
A central limit theorem for Stochastic Algorithms using Chen's projections, Preprint, CREMICS/ENPC, May 2006, n^o 312
http://cermics.enpc.fr/~lelong/research/papers/unpublished/tcl_proj.pdf.
[37]: J. Lelong.
Central Limit Theorems for Truncating and Averaging Stochastic Algorithms: a functional approach, Preprint, CREMICS/ENPC, May 2006, n^o 312
http://cermics.enpc.fr/reports/CERMICS-2006/CERMICS-2006-312.pdf.
[38]: H. Luschgy, G. Pagès.
Functional quantization rate and mean pathwise regularity of processes with an application to Lévy processes, Prepublication, University Paris VI, 2006, n^o PMA-1048.
[39]: H. Luschgy, G. Pagès.
Moment estimates for Lévy processes, Prepublication, University Paris VI, 2006, n^o PMA-1087.
[40]: B. Øksendal, A. Sulem.
A game theoretic approach to martingale measures in incomplete markets, eprint, Oslo University, October 2006, n^o 24
http://www.math.uio.no/eprint/pure_math/2006/24-06.html.

Miscellaneous

[41]: B. Fernández, D. Hernandez-Hernandez, A. Meda, P. Saavedra.
An optimal investment strategy with maximal risk aversion and its ruin probability, submitted.
[42]: D. Hernandez-Hernandez, M. Quenez.
Variance optimal martingale measure in a general stochastic volatility model, Preprint, 2006.
[43]: D. Lamberton, G. Pagès.
A penalized bandit algorithm, submitted for publication.
[44]: D. Lamberton, G. Pagès.
How fast is the bandit?, submitted for publication.
[45]: D. Lamberton, M. Zervos.
On the problem of optimally stopping a one-dimensional Ito diffusion, submitted for publication.
[46]: B. Øksendal, A. Sulem.
An anticipative stochastic calculus approach to pricing in markets driven by Lévy processes, manuscript.

References in notes

[47]: L. Andersen, R. Brotherton-Ratcliffe.
Extended Libor market models with stochastic volatility, in: Journal of Computational Finance, 2005, vol. 9, n^o 1.
[48]: L. Andersen, J. Sidenious.
Extension to the Gaussian Copula: Random Recovery and Random Factor Loadings, 2004.
[49]: V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria, Rocquencourt, February 2003, n^o 4718
http://hal.inria.fr/inria-00071868.
[50]: D. Bell.
The Malliavin Calculus, Pitman Monographs and Surveys in Pure and Applied Math., Longman and Wiley, 1987, n^o 34.
[51]: A. Beskos, G. O. Roberts.
Exact simulation of diffusions, in: Ann. Appl. Probab., 2005, vol. 15, n^o 4, p. 2422–2444.
[52]: F. Biagini, Y. Hu, B. Øksendal, A. Sulem.
A stochastic maximum principle for processes driven by fractional Brownian motion, in: Stochastic Processes and their applications, 2002, vol. 100, p. 233 - 253
http://www.math.uio.no/eprint/pure_math/2000/24-00.html.
[53]: F. Biagini, B. Øksendal, A. Sulem, N. Wallner.
An Introduction to white noise theory and Malliavin Calculus for Fractional Brownian Motion, in: Proc. Royal Society, special issue on stochastic analysis and applications, 2004, vol. 460, n^o 2041, p. 347–372.
[54]: F. Black, E. Derman, W. Toy.
A one factor model of interest rates and its application to treasury bond options, in: Financial Analysts Journal, January-February 1990.
[55]: A. Brace, D. Gatarek, M. Musiela.
The Market Model of Interest Rate Dynamics, in: Mathematical Finance, 1997, vol. 7, p. 127-156.
[56]: D. Brigo, M. Morini.
An empirically effcient analytical cascade calibration of the LIBOR Market Model based only on directly quoted swaptions data, 2005.
[57]: X. Burtschell, J. Laurent, J. Gregory.
A comparative analysis of CDO pricing models, 2005.
[58]: R. Carmona, N. Touzi.
Optimal multiple stopping and valuation of swing options, preprint.
[59]: J. C. Cox, J. E. Ingersoll, S. A. Ross.
A Theory of the Term Structure of Interest Rate, in: Econometrica, 1985, vol. 53, p. 363-384.
[60]: D. Duffie, L. Epstein.
Stochastic differential utility and asset pricing, in: Econometrica, 1992, vol. 60, p. 353-394.
[61]: E. Eberlein, W. Kluge.
Exact pricing formulae for caps and swaptions in a Lévy term structure model, in: Journal of Computational Finance, 2005, vol. 9, n^o 2.
[62]: E. Eberlein, F. Ozkan.
The Lévy LIBOR Model, in: Finance and Stochastics, 2005, vol. 9, p. 327-348.
[63]: E. Fournié, J.-M. Lasry, J. Lebuchoux, P.-L. Lions.
Applications of Malliavin calculus to Monte Carlo methods in Finance, II, in: Finance & Stochastics, 2001, vol. 2, n^o 5, p. 201-236.
[64]: E. Fournié, J.-M. Lasry, J. Lebuchoux, P.-L. Lions, N. Touzi.
An application of Malliavin calculus to Monte Carlo methods in Finance, in: Finance & Stochastics, 1999, vol. 4, n^o 3, p. 391-412.
[65]: M. Griebel.
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences, in: Computing, 1998, vol. 6, n^o 2, p. 151–179.
[66]: M. Griebel, P. Oswald.
Tensor-product-type subspace splittings and multilevel iterative methods for anisotropic problems, in: Advances of Computational Mathematics, 1995, vol. 4, p. 171–206.
[67]: N. Hilber, A. M. Matache, C. Schwab.
Sparse wavelet methods for option pricing under stochastic volatility, in: Journal of Computational Finance, 2005, vol. 8, n^o 4, p. 1-42.
[68]: Y. Hu, B. Øksendal, A. Sulem.
Optimal portfolio in a fractional Black & Scholes market, in: Mathematical Physics and Stochastic Analysis, S. Albeverio (editor), Essays in Honour of Ludwig Streit, World Scientific, 2000, p. 267-279
http://www.math.uio.no/eprint/pure_math/1999/13-99.html.
[69]: J. Hull, A. White.
Valuation of a CDO and an n^th to default CDS without Monte Carlo simulation, in: Journal of Derivatives, 2004, vol. 2, p. 8-23.
[70]: J. Hull, A. White.
Numerical Procedures for Implementing Term Structure Models I:Single Factor Models, in: Journal of Derivatives, 1994, vol. 2, p. 7-16.
[71]: P. Jaillet, E. Ronn, S. Tompaidis.
Valuation of Commodity-Based Swing Options, preprint
http://web.mit.edu/jaillet/www/general/swing-last.pdf.
[72]: A. Kolodko, J. Schoenmakers.
Iterative Construction of Optimal Bermudan stopping time, in: Finance and Stochastics, 2005, vol. 10, n^o 3, p. 27-49.
[73]: D. Lamberton, B. Lapeyre, A. Sulem.
Application of Malliavin Calculus to Finance, in: special issue of Mathematical Finance, January 2003.
[74]: B. Lapeyre, A. Sulem, D. Talay.
Simulation of Financial Models: Mathematical Foundations and Applications., to appear, Cambridge University Press.
[75]: J. Laurent, J. Gregory.
Basket Default Swaps, CDO's and Factor Copulas, Preprint, 2003.
[76]: S. Levendroskii, O. Kudrayavtsev, V. Zherder.
The relative efficency of numerical methods for pricing American options under Lévy Processes, in: Journal of Computational Finance, June 2005, vol. 9, n^o 2, p. 69-97.
[77]: P. Malliavin.
Stochastic calculus of variations and hypoelliptic operators, in: Proc.Inter.Symp. on Stoch.Diff. Equations, Kyoto, Wiley 1978, 1976, p. 195-263.
[78]: P. Malliavin, A. Thalmaier.
Stochastic Calculus of variations in Mathematical Finance, Springer Finance, Springer, 2006.
[79]: D. Nualart.
The Malliavin Calculus and Related Topics, Springer–Verlag, 1995.
[80]: D. Ocone, I. Karatzas.
A generalized representation formula with application to optimal portfolios, in: Stochastics and Stochastic Reports, 1991, vol. 34, p. 187-220.
[81]: D. Ocone.
A guide to the stochastic calculus of variations, in: Stochastic Analysis and Related Topics, H. Koerzlioglu, S. Üstünel (editors), Lecture Notes in Math.1316, 1987, p. 1-79.
[82]: F. Russo, P. Vallois.
Stochastic calculus with respect to continuous finite quadratic variation processes, in: Stochastics and Stochastics Reports, 2000, vol. 70, p. 1–40.
[83]: J. Schoenmakers.
Calibration of LIBOR models to caps and swaptions: a way around intrinsic instabilities via parsimonious structures and a collateral market criterion, Preprint, Weierstrass Institute, 2003.
[84]: O. Vasicek.
An Equilibrium Characterisation of Term Strucuture, in: Journal of Financial Economics, 1977, vol. 5, p. 177-188.
[85]: T. von Petersdorff, C. Schwab.
Numerical Solution of Parabolic Equations in High Dimensions, in: Mathematical Modelling and Numerical Analysis, 2004, vol. 38, n^o 1, p. 93–128.
[86]: L. Wu.
Fast at-the-money calibration of the Libor market model using Lagrange multipliers, in: Journal of Computational Finance, 2002, vol. 6, n^o 2.
[87]: C. Zenger.
Sparse Grids, in: Parallel Algortihms for PDE, Vieweg, Braunschweig, W. Hackblush (editor), 1991, vol. Proc. 6th GAMM Seminar, Kiel, p. 241-251.
[88]: B. Øksendal.
An Introduction to Malliavin Calculus with Applications to Economics, in: Lecture Notes from a course given 1996 at the Norwegian School of Economics and Business Administration (NHH), NHH Preprint Series, September 1996.

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