arXiv subjects

Vincent Lemaire

Publications and source records attributed to Vincent Lemaire.

62 records · Page 4Linked to original sources

arXiv2015

Increasing loyalty using predictive modeling in Business-to-Business Telecommunication

Customer Relationship Management (CRM) is a key element of modern marketing strategies. One of the most practical way to build useful knowledge on customers in a CRM system to produce scores to forecast churn behavior, propensity to subscribe to a new service... In AMEA zone (Asia, Middle East and Africa zone), the context of fierce competition may represent a higher percentage, and particularly in B2B market. But by contrast, to our knowledge, no scientific papers were dedicated and published to detail the way to improve loyalty in B2B Telco market. If we can assume at low segments similarities between B2B and B2C, some research is required in order to model B2B user behavior versus B2C behavior. This problematic stands actual as "Bring Your own Device" (BYOD) becomes more and more trendy. Answering business requirements, our team applied some B2C predictive tools with adapting them to B2B in an AMEA country Orange affiliate.

cs.OH↗

arXiv2014

Invariant distribution of duplicated diffusions and application to Richardson-Romberg extrapolation

With a view to numerical applications we address the following question: given an ergodic Brownian diffusion with a unique invariant distribution, what are the invariant distributions of the duplicated system consisting of two trajectories? We mainly focus on the interesting case where the two trajectories are driven by the same Brownian path. Under this assumption, we first show that uniqueness of the invariant distribution (weak confluence) of the duplicated system is essentially always true in the one-dimensional case. In the multidimensional case, we begin by exhibiting explicit counter-examples. Then, we provide a series of weak confluence criterions (of integral type) and also of a.s. pathwise confluence, depending on the drift and diffusion coefficients through a non-infinitesimal Lyapunov exponent. As examples, we apply our criterions to some non-trivially confluent settings such as classes of gradient systems with non-convex potentials or diffusions where the confluence is generated by the diffusive component. We finally establish that the weak confluence property is connected with an optimal transport problem. As a main application, we apply our results to the optimization of the Richardson-Romberg extrapolation for the numerical approximation of the invariant measure of the initial ergodic Brownian diffusion.

math.PR↗

arXiv2010

Joint Modelling of Gas and Electricity spot prices

The recent liberalization of the electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this paper, we modelize jointly gas and electricity spot prices using a mean-reverting model which fits the correlations structures for the two commodities. The dynamics are based on Ornstein processes with parameterized diffusion coefficients. Moreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions which captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. The associated calibration procedure is based on standard and efficient statistical tools. We calibrate the model on French market for electricity and on UK market for gas, and then simulate some trajectories which reproduce well the observed prices behavior. Finally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio.

q-fin.ST↗

arXiv2010

On some Non Asymptotic Bounds for the Euler Scheme

We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This Gaussian concentration is derived from a Gaussian upper bound of the density of the scheme and a modification of the so-called "Herbst argument" used to prove Logarithmic Sobolev inequalities. We eventually establish a Gaussian lower bound for the density of the scheme that emphasizes the concentration is sharp.

math.PR↗

arXiv2009

Unconstrained Recursive Importance Sampling

We propose an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations. We consider different parametric families based on the Girsanov theorem and the Esscher transform (or exponential-tilting). In a multidimensional Gaussian framework, Arouna uses a projected Robbins-Monro procedure to select the parameter minimizing the variance. In our approach, the parameter (scalar or process) is selected by a classical Robbins-Monro procedure without projection or truncation. To obtain this unconstrained algorithm we intensively use the regularity of the density of the law without assume smoothness of the payoff. We prove the convergence for a large class of multidimensional distributions and diffusion processes. We illustrate the effectiveness of our algorithm via pricing a Basket payoff under a multidimensional NIG distribution, and pricing a barrier options in different markets.

math.PR↗

arXiv2006

Sequential recruitment and combinatorial assembling of multiprotein complexes in transcriptional activation

In human cells, estrogenic signals induce cyclical association and dissociation of specific proteins with the DNA in order to activate transcription of estrogen-responsive genes. These oscillations can be modeled by assuming a large number of sequential reactions represented by linear kinetics with random kinetic rates. Application of the model to experimental data predicts robust binding sequences in which proteins associate with the DNA at several different phases of the oscillation. Our methods circumvent the need to derive detailed kinetic graphs, and are applicable to other oscillatory biological processes involving a large number of sequential steps.

q-bio.CB↗

arXiv2006

Behavior of the Euler scheme with decreasing step in a degenerate situation

The aim of this paper is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the diffusion coefficient are vanish simultaneously. As a first step, we give a brief description of the Feller's classification of the one-dimensional process. We recall the concept of attractive and repulsive boundary point and introduce the concept of strongly repulsive point. That allows us to establish a classification of the ergodic behavior of the diffusion. We conclude this section by giving necessary and sufficient conditions on the nature of boundary points in terms of Lyapunov functions. In the second section we use this characterization to study the decreasing step Euler scheme. We give also an numerical example in higher dimension.

math.PR↗

arXiv2005

An adaptive scheme for the approximation of dissipative systems

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit Euler scheme are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.

math.PR↗