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. Lapeyre, A. Sulem, D. Talay.
Simulation of Financial Models: Mathematical Foundations and Applications, Cambridge University Press, in final form.
B. Øksendal, A. Sulem.
Applied Stochastic Control of Jump Diffusions, Universitext, Springer Verlag , Berlin, Heidelberg, New York, 2005,11855,5-40109-22-34667289-0,00.html.

Doctoral dissertations and Habilitation theses

S. Hénon.
Modélisation de la courbe des taux en marché incomplet et calibration de modèles, Ph. D. Thesis, Université Marne la Vallée, September 2005.
A. Kbaier.
Réduction de variance et discrétisation d'équations différentielles stochastiques. Théorèmes limites presque sures pour les martingales quasi-continues à gauche., Ph. D. Thesis, Université Marne la Vallée, December 2005.
V. Lemaire.
Estimation récursive de la mesure invariante d'un processus de diffusion, Phd Thesis, Université Marne la Vallée, December 2005.
M. Messaoud.
Contrôle optimal stochastique et calcul de Malliavin appliqués à la finance., Ph. D. Thesis, Université Paris Dauphine, January 2006.
N. Moreni.
Méthodes de Monte Carlo et pricing d'options, Ph. D. Thesis, Université Paris VI, December 2005.

Articles in refereed journals and book chapters

A. Alfonsi.
On the discretization schemes for the CIR (and Bessel squared) processes, in: Monte Carlo Methods and Applications, 2005, p. 355-384.
A. Alfonsi, D. Brigo.
New Families of Copulas Based on Periodic Functions, in: Communications in Statistics: Theory and Methods, vol. 34, no 7, p. 1437-1447.
F. Antonelli, A. Kohatsu-Higa.
Densities of one dimensional backward SDE's, in: Potential Analysis, 2005, vol. 22, no 3, p. 263-287.
V. Bally.
Lower bounds for the density of Ito processes, in: Annals of Probability, to appear.
V. Bally, M. Caballero, B. Fernandez, N. El Karoui.
Reflected BSDE's , PDE's and Variational Inequalities, in: Bernoulli, to appear.
V. Bally, L. Caramelino, A. Zanette.
Pricing and hadging American options by Monte Carlo methods using Malliavin calculus approach, in: Monte Carlo methods, to appear.
V. Bally, G. Pagès, J. Printems.
A quantization tree method method for pricing and hedging multidimensional American options, in: Mathematical Finance, January 2005, vol. 15, no 1, p. 119–169.
V. Bally, E. Pardoux, L. Stoica.
Backward stochastic differential equations associated to symmetric Markov processes, in: Potential Theory, to appear
V. Bally, E. Pardoux, L. Stoica.
Backward stochastic differential equations associated to symmetric Markov processes, in: Potential Analysis, 2005, vol. 22, p. 17–60.
G. Bormetti, G. Montagna, N. Moreni, O. Nicrosini.
Pricing Exotic Options in a Path Integral Approach, in: Quantitative Finance, to appear.
D. Brigo, A. Alfonsi.
Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model, in: Finance and Stochastics, 2005, vol. 9, no 1, p. 29-42.
E. Chevalier.
Optimal early retirement near the expiration of a pension plan, in: Finance and Stochastics, forthcoming.
E. Chevalier.
Critical Price near maturity for an American Option on a dividend-paying stock in a local volatility model, in: Mathematical Finance, July 2005, vol. 15, no 3, p. 439–463.
E. Clément, A. Kohatsu-Higa, D. Lamberton.
A duality approach for the weak approximation of stochastic differential equations, in: Annals of Applied Probability, To appear.
R. Cont, P. Tankov.
Retrieving Lévy processes from option prices: regularization of an ill-posed inverse problem, in: SIAM Journal on Control and Optimization, to appear.
J. Guyon.
Euler Scheme and Tempered Distributions, in: Stochastic Processes and Their Applications, to appear
J. Kallsen, P. Tankov.
Characterization of dependence of multidimensional Lévy processes using Lévy copulas, in: Journal of Multivariate Analysis, to appear.
A. Kbaier.
Statistical Romberg approximation: a new variance reduction method and applications to option pricing, in: Annals of Applied Probability, forthcoming.
A. Kohatsu-Higa, A. Sulem.
Utility maximization in an insider influenced market, in: Mathematical Finance, 2006, vol. 16, no 1, p. 153–179
D. Lamberton, E. Clément, A. Kohatsu-Higa.
A duality approach for the weak approximation of stochastic differential equations, in: Annals of Applied Probability, to appear.
V. Lemaire.
An adaptive scheme for the approximation of dissipative systems, in: Stochastic Processes and Applications, accepted for publication.
M. Mnif, A. Sulem.
Optimal risk control and dividend policies under excess of loss reinsurance, in: Stochastics and Stochastic Reports, October 2005, vol. 77, no 5, p. 455-476.
M. N'Zi, Y. Ouknine, A. Sulem.
Regularity and representation of viscosity solutions of PDEs via BSDEs, in: Stochastic processes and their applications, accepted for publication.
G. Pagès, J. Printems.
Functional quantization for numerics with an application to option pricing, in: Monte Carlo Methods and Appl., to appear.

Publications in Conferences and Workshops

A. Alfonsi, E. Cancès, G. Turinici, B. Di Ventura, W. Huisinga.
Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems, in: ESAIM Proceedings, Math. and appl. to biology and medicine, September 2005, vol. 14
R. Cont, P. Tankov, E. Voltchkova.
Hedging with options in models with jumps, in: Proceedings of the II Abel Symposium 2005 on Stochastic analysis and applications, Oslo, accepted, Springer, 2005.
J. Guyon, A. Bize, G. Paul, E. Stewart, J. Delmas, F. Taddéi.
Statistical study of cellular aging, 2005, vol. 14, p. 100-114.
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), Proceedings Ritsumeikan International Symposium, Japan, March 2005, to appear, World Scientific.
P. Tankov.
Simulation and option pricing in Lévy copula model, in: Mathematical Modelling of Financial Derivatives, M. Avellaneda, R. Cont (editors), Springer, 2005, vol. IMA volumes in Mathematics and Applications.

Internal Reports

V. Bally, M. Bavouzet, M. Messaoud.
Integration by parts formula for locally smooth laws and applications to sensitivity computations, 54 pages, submitted to Annals of Applied Probabilities, INRIA , Rocquencourt, May 2005, no RR-5567
M. Bavouzet, M. Messaoud.
Computation of Greeks using Malliavin's calculus in jump type market models, 31 pages, INRIA , Rocquencourt, February 2005, no RR-5482
G. Di Nunno, A. Kohatsu-Higa, T. Meyer-Brandis, B. Øksendal, F. Proske, A. Sulem.
Optimal portfolio for a "large" insider in a market driven by Lévy Processes, Research paper, University of Oslo, 2005
B. Jourdain, A. Zanette.
A Moments and Strike Matching Binomial Algorithm for Pricing American Put Options, Research Report, INRIA , Rocquencourt, 2005, no 5569
J. Lelong.
A central limit theorem for Robbins Monro algorithms with projections, Technical report, ENPC/CERMICS, September 2005, no 2005-285.
F. Mercurio, N. Moreni.
Pricing Inflation-Indexed Options with Stochastic Volatility, submitted for publication, Financial Engineering group, Banca IMI , Milan.
B. Øksendal, A. Sulem.
Optimal stochastic impulse control with delayed reaction, Technical report, University of Oslo, 2005


R. Cont, P. Tankov, E. Voltchkova.
Hedging options in presence of jumps, Working Paper, 2005.
A. Debussche, J. Printems.
On the weak approximation of parabolic stochastic partial differential equations, working paper, 2005.
D. Lamberton, G. Pagès.
A penalized bandit algorithm, submitted for publication, 2005.
D. Lamberton, G. Pagès.
How fast is the bandit?, submitted for publication, 2005.
M. Messaoud, J. Da Fonseca.
Malliavin calculus for the Libor Market Model, Preprint, 2005.

References in notes

L. Andersen.
Volatility Skews and Extension of the LIBOR Market Models, in: Applied Mathematical Finance, 2000, vol. 7, p. 1-32.
L. Andersen.
A simple approach to the pricing of Bermudan swaptions in the multifactor LIBOR market model, in: Journal of Computational Finance, 1999, vol. 3, no 2, p. 5-32.
J. Andreasen.
The pricing of discretely sampled asian and lookback options: a change of numeraire approach, in: Journal of Computational Finance, 1998, vol. 1-2, p. 5-23.
B. Arouna.
Robbins-Monro algorithms and Variance reduction in finance, in: Journal of Computational Finance, Winter 2003/2004, vol. 7, no 2, p. 35–61.
V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria , Rocquencourt, February 2003, no 4718
V. Bally, G. Pagès.
A quantization algorithm for solving multidimensional discrete-time Optimal Stopping problems, in: Bernoulli, 2003, vol. 9, no 6, p. 1003–1049.
V. Bally, G. Pagès.
Error analysis of the quantization algorithm for obstacle problems, in: Stoch. Processes and their Applications, 2003, vol. 106, no 1, p. 1–40.
D. Bell.
The Malliavin Calculus, Pitman Monographs and Surveys in Pure and Applied Math., Longman and Wiley, 1987, no 34.
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.
H. Bungartz, M. Griebel.
Sparse grids, in: Acta Numerica, 2004.
P. Carr, D. Madan.
Option valuation using the fast Fourier transform, in: J. Comput. Finance, 1998.
P. Cohort.
Monte–Carlo methods for Pricing American Style Options, part of the documentation of Premia 3, 2001.
P. Collin-Dufresne, R. Goldstein.
Pricing Swaptions within an affine framework, in: The Journal of Derivatives, Fall 2002, p. 1-18.
R. Cont, P. Tankov.
Financial Modelling with Jump Processes, CRC Press, Chapman & Hall, 2004.
R. Cont, E. Voltchkova.
A finite difference scheme for option pricing in jump diffusion and exponential Lévy models, in: SIAM Journal on Numerical Analysis, 2005, vol. 43, no 4, p. 1596–1626.
J. Cox, J. Ingersoll, S. 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.
Y. Elouerkhaoui.
Correlation of Correlation, 2004, Working Paper.
Y. Elouerkhaoui.
Credit Derivatives: Basket Asymptotics, 2004, Working Paper.
Y. Elouerkhaoui.
Credit Risk: Quadratic Hedging, 2004, Working Paper.
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.
P. Glassermann, N. Merener.
Numerical solution of jump-diffusion LIBOR market models, in: Finance and Stochastics, 7, p. 1-27.
E. Gobet, G. Pagès, H. Pham, J. Printems.
Discretization and simulation for a class of SPDEs with applications to Zakai and McKean–Vlasov equations, 2004, working paper.
Y. Hu, B. Øksendal, A. Sulem.
Mathematical Physics and Stochastic Analysis, S. Albeverio, et al. (editors), Essays in Honour of Ludwig Streit, World Scientific, 2000, chap. Optimal portfolio in a fractional Black & Scholes market, p. 267-279
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.
J. Kennedy, P. Hunt, A. Pelsser.
Markov-functional interest rate models, in: Finance and Stochastics, 2000, vol. 4, no 4, p. 391-408.
D. Lamberton, B. Lapeyre, A. Sulem.
Application of Malliavin Calculus to Finance, in: special issue of Mathematical Finance, January 2003.
D. Lamberton, G. Pagès.
Recursive computation of the invariant measure of a diffusion: the case of a weakly mean reverting drift, in: Stochastics and dynamics, 2003, vol. 4, p. 431–451.
D. Lamberton, S. Villeneuve.
Critical price near maturity for an american option on a dividend paying stock, in: Annals of Applied Probability, 2003, vol. 13, p. 800–815.
J. Laurent, J. Gregory.
Basket Default Swaps, CDO's and Factor Copulas, Preprint, 2003.
R. Lee.
Option pricing by transform methods: extensions, unification and error control, in: J. Comput. Finance, 2004, vol. 7.
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.
S. Ninomiya, N. Victoir.
Weak Approximation and Derivative Pricing, Preprint, 2005.
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.
G. Pagès, H. Pham, J. Printems.
An Optimal Markovian Quantization Algorithm for Multidimensional Stochastic Control Problems, in: Stochastics and Dynamics, 2004, vol. 4, no 4, p. 501–545.
H. Pham, G. Pagès, J. Printems.
Handbook of Computational and Numerical Methods in Finance, S. Rachev (editor), Birkhauser , Boston, 2004, chap. Optimal quantization methods and applications to numerical problems in finance, p. 253–298.
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.
P. Schonbucher.
A tree implementation of a credit spread model for credit derivatives, in: Journal of Computational Finance, 2002, vol. 6, no 2.
P. Tankov.
Lévy Processes in Finance: Inverse Problems and Dependence Modelling, PhD thesis, Ecole Polytechnique, 2004.
J. Van Ginderen, H. Garcia, R. Source.
On the Pricing of Credit Spread Options: A Two Factor HW?BK Algorithm.International Journal of Theoretical, in: Applied Finance, August 2003, vol. 6, no 5.
O. Vasicek.
An Equilibrium Characterisation of Term Strucuture, in: Journal of Financial Economics, 1977, vol. 5, p. 177-188.
E. Voltchkova.
Integro-differential evolution equations: numerical methods and applications in finance, PhD thesis, Ecole Polytechnique, Paris, 2005
T. von Petersdorff, C. Schwab.
Numerical Solution of Parabolic Equations in High Dimensions, Preprint, 2004.
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.