Team Mathfi

Members
Overall Objectives
Scientific Foundations
Application Domains
Software
New Results
Contracts and Grants with Industry
Dissemination
Bibliography

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, no 2, p. 153–188.
[2]
B. Arouna.
Adaptative Monte Carlo Method, A Variance Reduction technique, in: Monte Carlo Methods and Applications, 2004, vol. 10, no 1.
[3]
V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria , Rocquencourt, February 2003, no 4718
http://www.inria.fr/rrrt/rr-4718.html.
[4]
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.
[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, no 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, no 1, p. 39-57.
[9]
D. Lefèvre.
An introduction to Utility Maximization with Partial Observation, in: Finance, 2002, vol. 23
http://www.inria.fr/rrrt/rr-4183.html.
[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, no 6, p. 1765–1790.

Publications of the year

Books and Monographs

[11]
B. Lapeyre, A. Sulem, D. Talay.
Simulation of Financial Models: Mathematical Foundations and Applications, Cambridge University Press, in final form.
[12]
B. Øksendal, A. Sulem.
Applied Stochastic Control of Jump Diffusions, Universitext, Springer Verlag , Berlin, Heidelberg, New York, 2005
http://www.springer.com/sgw/cda/frontpage/0,11855,5-40109-22-34667289-0,00.html.

Doctoral dissertations and Habilitation theses

[13]
S. Hénon.
Modélisation de la courbe des taux en marché incomplet et calibration de modèles, Ph. D. Thesis, Université Marne la Vallée, September 2005.
[14]
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.
[15]
V. Lemaire.
Estimation récursive de la mesure invariante d'un processus de diffusion, Phd Thesis, Université Marne la Vallée, December 2005.
[16]
M. Messaoud.
Contrôle optimal stochastique et calcul de Malliavin appliqués à la finance., Ph. D. Thesis, Université Paris Dauphine, January 2006.
[17]
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

[18]
A. Alfonsi.
On the discretization schemes for the CIR (and Bessel squared) processes, in: Monte Carlo Methods and Applications, 2005, p. 355-384.
[19]
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.
[20]
F. Antonelli, A. Kohatsu-Higa.
Densities of one dimensional backward SDE's, in: Potential Analysis, 2005, vol. 22, no 3, p. 263-287.
[21]
V. Bally.
Lower bounds for the density of Ito processes, in: Annals of Probability, to appear.
[22]
V. Bally, M. Caballero, B. Fernandez, N. El Karoui.
Reflected BSDE's , PDE's and Variational Inequalities, in: Bernoulli, to appear.
[23]
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.
[24]
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.
[25]
V. Bally, E. Pardoux, L. Stoica.
Backward stochastic differential equations associated to symmetric Markov processes, in: Potential Theory, to appear
http://www.inria.fr/rrrt/rr-4425.html.
[26]
V. Bally, E. Pardoux, L. Stoica.
Backward stochastic differential equations associated to symmetric Markov processes, in: Potential Analysis, 2005, vol. 22, p. 17–60.
[27]
G. Bormetti, G. Montagna, N. Moreni, O. Nicrosini.
Pricing Exotic Options in a Path Integral Approach, in: Quantitative Finance, to appear.
[28]
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.
[29]
E. Chevalier.
Optimal early retirement near the expiration of a pension plan, in: Finance and Stochastics, forthcoming.
[30]
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.
[31]
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.
[32]
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.
[33]
J. Guyon.
Euler Scheme and Tempered Distributions, in: Stochastic Processes and Their Applications, to appear
http://cermics.enpc.fr/~guyon/home.html.
[34]
J. Kallsen, P. Tankov.
Characterization of dependence of multidimensional Lévy processes using Lévy copulas, in: Journal of Multivariate Analysis, to appear.
[35]
A. Kbaier.
Statistical Romberg approximation: a new variance reduction method and applications to option pricing, in: Annals of Applied Probability, forthcoming.
[36]
A. Kohatsu-Higa, A. Sulem.
Utility maximization in an insider influenced market, in: Mathematical Finance, 2006, vol. 16, no 1, p. 153–179
http://www.inria.fr/rrrt/rr-5379.html.
[37]
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.
[38]
V. Lemaire.
An adaptive scheme for the approximation of dissipative systems, in: Stochastic Processes and Applications, accepted for publication.
[39]
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.
[40]
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.
[41]
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

[42]
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
http://www.edpsciences.org/articles/proc/abs/2005/01/contents/contents.html.
[43]
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.
[44]
J. Guyon, A. Bize, G. Paul, E. Stewart, J. Delmas, F. Taddéi.
Statistical study of cellular aging, 2005, vol. 14, p. 100-114.
[45]
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.
[46]
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

[47]
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
http://www.inria.fr/rrrt/rr-5567.html.
[48]
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
http://www.inria.fr/rrrt/rr-5482.html.
[49]
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
http://www.math.uio.no/eprint/pure_math/2005/pure_2005.html.
[50]
B. Jourdain, A. Zanette.
A Moments and Strike Matching Binomial Algorithm for Pricing American Put Options, Research Report, INRIA , Rocquencourt, 2005, no 5569
http://www.inria.fr/rrrt/rr-5569.html.
[51]
J. Lelong.
A central limit theorem for Robbins Monro algorithms with projections, Technical report, ENPC/CERMICS, September 2005, no 2005-285.
[52]
F. Mercurio, N. Moreni.
Pricing Inflation-Indexed Options with Stochastic Volatility, submitted for publication, Financial Engineering group, Banca IMI , Milan.
[53]
B. Øksendal, A. Sulem.
Optimal stochastic impulse control with delayed reaction, Technical report, University of Oslo, 2005
http://www.math.uio.no/eprint/pure_math/2005/27-05.html.

Miscellaneous

[54]
R. Cont, P. Tankov, E. Voltchkova.
Hedging options in presence of jumps, Working Paper, 2005.
[55]
A. Debussche, J. Printems.
On the weak approximation of parabolic stochastic partial differential equations, working paper, 2005.
[56]
D. Lamberton, G. Pagès.
A penalized bandit algorithm, submitted for publication, 2005.
[57]
D. Lamberton, G. Pagès.
How fast is the bandit?, submitted for publication, 2005.
[58]
M. Messaoud, J. Da Fonseca.
Malliavin calculus for the Libor Market Model, Preprint, 2005.

References in notes

[59]
L. Andersen.
Volatility Skews and Extension of the LIBOR Market Models, in: Applied Mathematical Finance, 2000, vol. 7, p. 1-32.
[60]
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.
[61]
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.
[62]
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.
[63]
V. Bally.
An elementary introduction to Malliavin calculus, Research Report, Inria , Rocquencourt, February 2003, no 4718
http://www.inria.fr/rrrt/rr-4718.html.
[64]
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.
[65]
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.
[66]
D. Bell.
The Malliavin Calculus, Pitman Monographs and Surveys in Pure and Applied Math., Longman and Wiley, 1987, no 34.
[67]
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.
[68]
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.
[69]
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.
[70]
A. Brace, D. Gatarek, M. Musiela.
The Market Model of Interest Rate Dynamics, in: Mathematical Finance, 1997, vol. 7, p. 127-156.
[71]
H. Bungartz, M. Griebel.
Sparse grids, in: Acta Numerica, 2004.
[72]
P. Carr, D. Madan.
Option valuation using the fast Fourier transform, in: J. Comput. Finance, 1998.
[73]
P. Cohort.
Monte–Carlo methods for Pricing American Style Options, part of the documentation of Premia 3, 2001.
[74]
P. Collin-Dufresne, R. Goldstein.
Pricing Swaptions within an affine framework, in: The Journal of Derivatives, Fall 2002, p. 1-18.
[75]
R. Cont, P. Tankov.
Financial Modelling with Jump Processes, CRC Press, Chapman & Hall, 2004.
[76]
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.
[77]
J. Cox, J. Ingersoll, S. Ross.
A Theory of the Term Structure of Interest Rate, in: Econometrica, 1985, vol. 53, p. 363-384.
[78]
D. Duffie, L. Epstein.
Stochastic differential utility and asset pricing, in: Econometrica, 1992, vol. 60, p. 353-394.
[79]
Y. Elouerkhaoui.
Correlation of Correlation, 2004, Working Paper.
[80]
Y. Elouerkhaoui.
Credit Derivatives: Basket Asymptotics, 2004, Working Paper.
[81]
Y. Elouerkhaoui.
Credit Risk: Quadratic Hedging, 2004, Working Paper.
[82]
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.
[83]
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.
[84]
P. Glassermann, N. Merener.
Numerical solution of jump-diffusion LIBOR market models, in: Finance and Stochastics, 7, p. 1-27.
[85]
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.
[86]
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
http://www.math.uio.no/eprint/pure_math/1999/13-99.html.
[87]
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.
[88]
J. Kennedy, P. Hunt, A. Pelsser.
Markov-functional interest rate models, in: Finance and Stochastics, 2000, vol. 4, no 4, p. 391-408.
[89]
D. Lamberton, B. Lapeyre, A. Sulem.
Application of Malliavin Calculus to Finance, in: special issue of Mathematical Finance, January 2003.
[90]
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.
[91]
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.
[92]
J. Laurent, J. Gregory.
Basket Default Swaps, CDO's and Factor Copulas, Preprint, 2003.
[93]
R. Lee.
Option pricing by transform methods: extensions, unification and error control, in: J. Comput. Finance, 2004, vol. 7.
[94]
P. Malliavin.
Stochastic calculus of variations and hypoelliptic operators, in: Proc.Inter.Symp. on Stoch.Diff. Equations, Kyoto, Wiley 1978, 1976, p. 195-263.
[95]
P. Malliavin, A. Thalmaier.
Stochastic Calculus of variations in Mathematical Finance, Springer Finance, Springer, 2006.
[96]
S. Ninomiya, N. Victoir.
Weak Approximation and Derivative Pricing, Preprint, 2005.
[97]
D. Nualart.
The Malliavin Calculus and Related Topics, Springer–Verlag, 1995.
[98]
D. Ocone, I. Karatzas.
A generalized representation formula with application to optimal portfolios, in: Stochastics and Stochastic Reports, 1991, vol. 34, p. 187-220.
[99]
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.
[100]
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.
[101]
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.
[102]
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.
[103]
P. Schonbucher.
A tree implementation of a credit spread model for credit derivatives, in: Journal of Computational Finance, 2002, vol. 6, no 2.
[104]
P. Tankov.
Lévy Processes in Finance: Inverse Problems and Dependence Modelling, PhD thesis, Ecole Polytechnique, 2004.
[105]
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.
[106]
O. Vasicek.
An Equilibrium Characterisation of Term Strucuture, in: Journal of Financial Economics, 1977, vol. 5, p. 177-188.
[107]
E. Voltchkova.
Integro-differential evolution equations: numerical methods and applications in finance, PhD thesis, Ecole Polytechnique, Paris, 2005
http://tel.ccsd.cnrs.fr/tel-00010842.
[108]
T. von Petersdorff, C. Schwab.
Numerical Solution of Parabolic Equations in High Dimensions, Preprint, 2004.
[109]
C. Zenger.
Sparse Grids, in: Parallel Algortihms for PDE, Vieweg, Braunschweig, W. Hackblush (editor), 1991, vol. Proc. 6th GAMM Seminar, Kiel, p. 241-251.
[110]
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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