Publications

2011

• Autostéréogramme d'une montagne gaussienne -utilisant une structure paradoxale périodique comme texture de camouflage
  
  • Colonna Jean-François
  , 2011. Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain (Autostéréogramme d'une montagne gaussienne -utilisant une structure paradoxale périodique comme texture de camouflage-)
• Montagne gaussienne
  
  • Colonna Jean-François
  , 2011. Gaussian Mountain (Montagne gaussienne)
• Interacting particle processes and approximation of Markov processes conditioned to not be killed
  
  • Villemonais Denis
  , 2011. We prove an approximation method for general strong Markov processes conditioned to not be killed. The method is based on a Fleming-Viot type interacting particle system, whose particles evolve as independent copies of the original strong Markov process and jump onto each others instead of being killed. We only assume that the number of jumps of the Fleming-Viot type system doesn't explode in finite time almost surely, and that the survival probability at fixed time of the original process is positive. We also give a speed of convergence for the approximation method. A criterion for the non-explosion of the number of jumps is then given for general systems of time and environment dependent diffusion particles, which includes the case of the Fleming-Viot type system of the approximation method. The proof of the criterion uses an original non-attainability of (0,0) result for a pair of non-negative semi-martingales with positive jumps.
• On the use of T-coercivity to study the interior transmission eigenvalue problem
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Haddar Houssem
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2011, 349 (11-12), pp.647-651. (10.1016/j.crma.2011.05.008)
  DOI : 10.1016/j.crma.2011.05.008
• MONTE CARLO APPROXIMATIONS OF AMERICAN OPTIONS THAT PRESERVE MONOTONICITY AND CONVEXITY
  
  • del Moral Pierre
  • Rémillard Bruno
  • Rubenthaler Sylvain
  , 2012, 12, pp.115-143. It can be shown that when the payoff function is convex and decreasing (re- spectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of the associated American option, provided some conditions are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve the convexity or monotonicity properties. In this paper, we propose a method of approximation for American options which can preserve both convexity and monotonicity. The resulting values can then be used to define exercise times and can also be used in combination with primal-dual methods to get sharper bounds. Other application of the algorithm include finding optimal hedging strategies. (10.1007/978-3-642-25746-9_4)
  DOI : 10.1007/978-3-642-25746-9_4
• Volatility dynamics
  
  • Nicolay David
  , 2011. We establish asymptotic links between two classes of stochastic volatility models describing the same derivative market : - a generic stochastic instantaneous volatility (SInsV) model, whose SDE system is a formal Wiener chaos without any specified state variable. - a sliding stochastic implied volatility (SImpV) class, another market model describing explicitly the joint dynamics of the underlying and of the associated European option surface. Each of these connections is achieved by layer, between a group of SInsV coefficients and set of (static and dynamic) SImpV differentials. The asymptotic approach leads to these cross-differentials being taken at the zero-expiry, At-The-Money point. We progress from a simple single-underlying and bi-dimensional setup, first to a multi-dimensional configuration, and then to a term-structure framework. We expose the structural modelling constraints and the asymmetry between the direct problem (from SInsV to SImpV) and the inverse one. We show that this Asymptotic Chaos Expansion (ACE) methodology is a powerful tool for model design and analysis. Focusing on local volatility models and their extensions, we compare ACE with the literature and exhibit a systematic bias in Gatheral's heuristics. In the multi-dimensional context we focus on stochastic-weights baskets, for which ACE provides intuitive results underlining the embedded induction. In the interest rates environment, we derive the first layer of smile descriptors for caplets, swaptions and bond options, within both a SV-HJM and a SV-LMM framework. Also, we prove that ACE can be automated for generic models, at any order, without formal calculus. The interest this algorithm is demonstrated by computing manually the 2nd and 3rd layers, in a generic bi-dimensional SInsV model. We present the applicative potential of ACE for calibration, pricing, hedging or relative value purposes, illustrated with numerical tests on the CEV-SABR model.
• Structure paradoxale -de l'ordre au désordre
  
  • Colonna Jean-François
  , 2011. Paradoxal structure -from Order to Disorder- (Structure paradoxale -de l'ordre au désordre-)
• Structure paradoxale
  
  • Colonna Jean-François
  , 2011. Paradoxal structure (Structure paradoxale)
• Structure paradoxale dans le ciel
  
  • Colonna Jean-François
  , 2011. Paradoxal structure in the sky (Structure paradoxale dans le ciel)
• Modelling microstructure noise with Hawkes processes
  
  • Bacry Emmanuel
  • Delattre Sylvain
  • Hoffmann Marc
  • Muzy J.-F.
  , 2011. Hawkes processes are used for modeling tick-by-tick variations of a single or of a pair of asset prices. For each asset, two counting processes (with stochastic intensities) are associated respectively with the positive and negative jumps of the price. We show that, by coupling these two intensities, one can reproduce high-frequencymean reversion structure that is characteristic of the microstructure noise. Moreover, in the case of two assets, by coupling the stochastic intensities corresponding to the positive (resp. negative) jumps of each asset, we are able to reproduce the Epps effect, i.e., the decorrelation of the increments at microscopic scales. At large scale our model becomes diffusive and converge towards a standard Brownian motion. Analytical closed-form formulae for the mean signature plot, the diffusive correlation matrix and the cross-asset correlation function at any time-scale are given. Empirical results are shown on futures Euro-Bund and Euro-Bobl high frequency data.
• A diffusion approximation theorem for a nonlinear PDE with application to random birefringent optical fibers.
  
  • de Bouard Anne
  • Gazeau Maxime
  , 2011. In this article, we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty, where a linear electric field is considered, and we get an asymptotic dynamic for the nonlinear electric field.
• Modélisation et simulation de la dynamique des globules rouges
  
  • Bui Cuc
  • Lleras Vanessa
  • Pantz Olivier
  , 2011, pp.Clé USB. See http://hal.archives-ouvertes.fr/docs/00/59/27/10/ANNEX/r_X358UUPX.pdf
• Problèmes de contact pour des particules en écoulement cisaillé
  
  • Verdon Nicolas
  • Laure Patrice
  • Lefebvre-Lepot Aline
  • Lobry Laurent
  , 2011, pp.Clé USB. See http://hal.archives-ouvertes.fr/docs/00/59/28/28/ANNEX/r_X8K316T9.pdf
• Univers ou Multivers -L'Univers fractal- ?
  
  • Colonna Jean-François
  , 2011. Universe or Multiverse -The fractal Universe- ? (Univers ou Multivers -L'Univers fractal- ?)
• Entrelacs
  
  • Colonna Jean-François
  , 2011. Intertwining (Entrelacs)
• Hierarchical clustering for graph visualization
  
  • Clémençon Stéphan
  • de Arazoza Hector
  • Rossi Fabrice
  • Tran Viet Chi
  , 2011, pp.227-232. This paper describes a graph visualization methodology based on hierarchical maximal modularity clustering, with interactive and significant coarsening and refining possibilities. An application of this method to HIV epidemic analysis in Cuba is outlined.
• Trou noir Paradoxal
  
  • Colonna Jean-François
  , 2011. Paradoxal black hole (Trou noir Paradoxal)
• Entrelacs
  
  • Colonna Jean-François
  , 2011. Intertwining (Entrelacs)
• Structure paradoxale basée sur la géométrie de la surface de Boy
  
  • Colonna Jean-François
  , 2011. Paradoxal structure based on the geometry of the Boy surface (Structure paradoxale basée sur la géométrie de la surface de Boy)
• Structure paradoxale basée sur la géométrie du plan
  
  • Colonna Jean-François
  , 2011. Paradoxal structure based on the geometry of the plane (Structure paradoxale basée sur la géométrie du plan)
• Random right eigenvalues of Gaussian quaternionic matrices
  
  • Benaych-Georges Florent
  • Chapon Francois
  , 2011. We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on more general Gaussian quaternionic random matrix models are also made.
• Structure paradoxale basée sur la géométrie de la triple bouteille de Bonan-Jeener-Klein
  
  • Colonna Jean-François
  , 2011. Paradoxal structure based on the geometry of the Bonan-Jeener's triple Klein bottle (Structure paradoxale basée sur la géométrie de la triple bouteille de Bonan-Jeener-Klein)
• Structure paradoxale basée sur la géométrie de la sphère
  
  • Colonna Jean-François
  , 2011. Paradoxal structure based on the geometry of the sphere (Structure paradoxale basée sur la géométrie de la sphère)
• Structure paradoxale basée sur la géométrie de la triple bouteille de Bonan-Jeener-Klein
  
  • Colonna Jean-François
  , 2011. Paradoxal structure based on the geometry of the Bonan-Jeener's triple Klein bottle (Structure paradoxale basée sur la géométrie de la triple bouteille de Bonan-Jeener-Klein)
• Structure paradoxale basée sur la géométrie de la surface de Boy
  
  • Colonna Jean-François
  , 2011. Paradoxal structure based on the geometry of the Boy surface (Structure paradoxale basée sur la géométrie de la surface de Boy)