Team Mathfi

Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry


Major publications by the team in recent years

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, no 2, p. 153–188.
B. Arouna.
Adaptative Monte Carlo Method, A Variance Reduction technique, in: Monte Carlo Methods and Applications, 2004, vol. 10, no 1.
V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria, Rocquencourt, February 2003, no 4718
V. Bally, G. Pagès, J. Printems.
First order schemes in the numerical quantization method, in: Mathematical Finance, 2003, vol. 13, no 1, p. 1–16.
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.
B. Jourdain, C. Martini.
American prices embedded in European prices, in: Annales de l'IHP, analyse non linéaire, 2001, vol. 18, no 1, p. 1-17.
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.
B. Lapeyre, E. Temam.
Competitive Monte-Carlo Methods for the Pricing of Asian Options, in: Journal of Computational Finance, 2001, vol. 5, no 1, p. 39-57.
D. Lefèvre.
An introduction to Utility Maximization with Partial Observation, in: Finance, 2002, vol. 23
B. Øksendal, A. Sulem.
Optimal Consumption and Portfolio with both fixed and proportional transaction costs, in: SIAM J. Control and Optim, 2002, vol. 40, no 6, p. 1765–1790.

Publications of the year

Books and Monographs

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

V. Bally.
Lower bounds for the density of a locally elliptic Ito process, in: Annals of Probability, to appear.
V. Bally, M. Bavouzet, M. Messaoud.
Computations of Gereks using Malliavin Calculus in jump type market models, in: Annals of Applied Probabilites, to appear.
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.
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
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, no 3, p. 1124-1154.
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.
S. Graf, H. Luschgy, G. Pagès.
Distortion mismatch in the quantization of probability measures, in: ESAIM PS, To appear.
S. Graf, H. Luschgy, G. Pagès.
Optimal quantizers for Radon random vectors in a Banach space, in: J. of Approximation, to appear.
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.
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.
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.
A. Kohatsu-Higa, A. Sulem.
Utility maximization in an insider influenced market, in: Mathematical Finance, 2006, vol. 16, no 1, p. 153–179.
H. Luschgy, G. Pagès.
Functional quantization of 1-dimensional Brownian diffusions, in: Stochastic Processes and their Applications, 2006, vol. 116, no 2, p. 310–336.
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, no 9, p. 1319–1339.
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

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.
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.
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.
Y. Ma, N. Privault.
FKG inequality on the Wiener space via predictable representation.

Internal Reports

A. Alfonsi, B. Jourdain.
A Call-Put Duality for Perpetual American Options, Preprint, CREMICS/ENPC, 2006, no 307.
D. David, N. Privault.
Numerical computation of Theta in a jump-diffusion model by integration by parts, Technical report, INRIA, 2006, no 32
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.
B. Jourdain.
Stochastic flows approach to Dupire's formula, Preprint, CREMICS/ENPC, 2006, no 326.
J. Lelong, C. Labart.
Pricing double barrier Parisian Options using Laplace transforms, Preprint, CREMICS/ENPC, 2006, no 328
J. Lelong.
A central limit theorem for Stochastic Algorithms using Chen's projections, Preprint, CREMICS/ENPC, May 2006, no 312
J. Lelong.
Central Limit Theorems for Truncating and Averaging Stochastic Algorithms: a functional approach, Preprint, CREMICS/ENPC, May 2006, no 312
H. Luschgy, G. Pagès.
Functional quantization rate and mean pathwise regularity of processes with an application to Lévy processes, Prepublication, University Paris VI, 2006, no PMA-1048.
H. Luschgy, G. Pagès.
Moment estimates for Lévy processes, Prepublication, University Paris VI, 2006, no PMA-1087.
B. Øksendal, A. Sulem.
A game theoretic approach to martingale measures in incomplete markets, eprint, Oslo University, October 2006, no 24


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

References in notes

L. Andersen, R. Brotherton-Ratcliffe.
Extended Libor market models with stochastic volatility, in: Journal of Computational Finance, 2005, vol. 9, no 1.
L. Andersen, J. Sidenious.
Extension to the Gaussian Copula: Random Recovery and Random Factor Loadings, 2004.
V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria, Rocquencourt, February 2003, no 4718
D. Bell.
The Malliavin Calculus, Pitman Monographs and Surveys in Pure and Applied Math., Longman and Wiley, 1987, no 34.
A. Beskos, G. O. Roberts.
Exact simulation of diffusions, in: Ann. Appl. Probab., 2005, vol. 15, no 4, p. 2422–2444.
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
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, no 2041, p. 347–372.
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.
A. Brace, D. Gatarek, M. Musiela.
The Market Model of Interest Rate Dynamics, in: Mathematical Finance, 1997, vol. 7, p. 127-156.
D. Brigo, M. Morini.
An empirically effcient analytical cascade calibration of the LIBOR Market Model based only on directly quoted swaptions data, 2005.
X. Burtschell, J. Laurent, J. Gregory.
A comparative analysis of CDO pricing models, 2005.
R. Carmona, N. Touzi.
Optimal multiple stopping and valuation of swing options, preprint.
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.
D. Duffie, L. Epstein.
Stochastic differential utility and asset pricing, in: Econometrica, 1992, vol. 60, p. 353-394.
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, no 2.
E. Eberlein, F. Ozkan.
The Lévy LIBOR Model, in: Finance and Stochastics, 2005, vol. 9, p. 327-348.
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, no 5, p. 201-236.
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, no 3, p. 391-412.
M. Griebel.
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences, in: Computing, 1998, vol. 6, no 2, p. 151–179.
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.
N. Hilber, A. M. Matache, C. Schwab.
Sparse wavelet methods for option pricing under stochastic volatility, in: Journal of Computational Finance, 2005, vol. 8, no 4, p. 1-42.
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
J. Hull, A. White.
Valuation of a CDO and an nth to default CDS without Monte Carlo simulation, in: Journal of Derivatives, 2004, vol. 2, p. 8-23.
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.
P. Jaillet, E. Ronn, S. Tompaidis.
Valuation of Commodity-Based Swing Options, preprint
A. Kolodko, J. Schoenmakers.
Iterative Construction of Optimal Bermudan stopping time, in: Finance and Stochastics, 2005, vol. 10, no 3, p. 27-49.
D. Lamberton, B. Lapeyre, A. Sulem.
Application of Malliavin Calculus to Finance, in: special issue of Mathematical Finance, January 2003.
B. Lapeyre, A. Sulem, D. Talay.
Simulation of Financial Models: Mathematical Foundations and Applications., to appear, Cambridge University Press.
J. Laurent, J. Gregory.
Basket Default Swaps, CDO's and Factor Copulas, Preprint, 2003.
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, no 2, p. 69-97.
P. Malliavin.
Stochastic calculus of variations and hypoelliptic operators, in: Proc.Inter.Symp. on Stoch.Diff. Equations, Kyoto, Wiley 1978, 1976, p. 195-263.
P. Malliavin, A. Thalmaier.
Stochastic Calculus of variations in Mathematical Finance, Springer Finance, Springer, 2006.
D. Nualart.
The Malliavin Calculus and Related Topics, Springer–Verlag, 1995.
D. Ocone, I. Karatzas.
A generalized representation formula with application to optimal portfolios, in: Stochastics and Stochastic Reports, 1991, vol. 34, p. 187-220.
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.
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.
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.
O. Vasicek.
An Equilibrium Characterisation of Term Strucuture, in: Journal of Financial Economics, 1977, vol. 5, p. 177-188.
T. von Petersdorff, C. Schwab.
Numerical Solution of Parabolic Equations in High Dimensions, in: Mathematical Modelling and Numerical Analysis, 2004, vol. 38, no 1, p. 93–128.
L. Wu.
Fast at-the-money calibration of the Libor market model using Lagrange multipliers, in: Journal of Computational Finance, 2002, vol. 6, no 2.
C. Zenger.
Sparse Grids, in: Parallel Algortihms for PDE, Vieweg, Braunschweig, W. Hackblush (editor), 1991, vol. Proc. 6th GAMM Seminar, Kiel, p. 241-251.
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.