Local Parametric Estimation in High Frequency Data

In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process $\Theta = T^{-1} \int_0^T \theta_t^* dt$. We provide a local parametric estimator (LPE) of $\Theta$ and conditions under which we can show the central limit theorem. Roughly speaking those conditions correspond to some uniform limit theory in the parametric version of the problem. The framework is restricted to the specific convergence rate $n^{1/2}$. Several examples of LPE are studied: estimation of volatility, powers of volatility, volatility when incorporating trading information and time-varying MA(1).Comment: 67 pages, 4 figure

Existence in the inverse Shiryaev problem

In this paper, we consider the inverse first-passage Shiryaev problem, i.e. for $(W_t)_{t \geq 0}$ a standard Brownian motion and any upper boundary continuous function $g: \mathbb{R}^+ \rightarrow \mathbb{R}$ satisfying $g(0) \geq 0$, we define $$\mathrm{T}_g^W := \inf \{t \in \mathbb{R}^+ \text{ s.t. } W_t \geq g(t)\},$$ and $f_g^W (t)$ its related density. For any target density function of the form $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ satisfying some smooth assumptions and any arbitrarily big horizon time $T > 0$, we show the existence of a related boundary $g_{f,T} : \mathbb{R}^+ \rightarrow [0,T]$, with $g_{f,T}(0) \geq 0$, which satisfies $$f_{g_{f,T}}^W (t) = f(t) \text{ for } 0 \leq t \leq T.$$ As an example, the exponential distribution $f(t) = \lambda \exp (- \lambda t)$ for $\lambda > 0$ satisfies the assumptions of this paper. As $g_{f,T}$ is exhibited as a limit boundary of a subsequence of a piecewise linear boundary, we do not obtain any explicit formula for $g_{f,T}$ as a function of $f$, nor the unicity of the solution. The results are also proved in the symmetrical two-dimensional boundary case

Three-dimensional study for the relative positioning of mechanical elements in mechanisms constituted by parrallel joints with clearances

The great evolution of the data-processing tools during the last years allowed for the development of the computer aided design in the field of mechanical structures. Controlling the clearance in joints between parts, is one of the required objectives to provide accurate relative movements and to minimize geometrical errors. For that purpose, a new method of static study allowing for the computation of the equilibrium positions of various elements in spatial mechanisms constituted by parallel joints and subjected to mechanical loadings is proposed. The isostatic study takes into account the presence of the clearance in the mechanism joints. The method is based to the minimization of the potential energy by means of some algorithms of optimization. The results obtained show the effectiveness of the method

Dejours, C. & Bègue, F. Suicide et travail : que faire ?

Ce petit livre de 125 pages, écrit à quatre mains par Christophe Dejours et Florence Bègue, expose son projet dans son titre : que faire avec les suicides au travail - quoi faire, comment faire, à partir de quoi faire ? C’est un texte orienté vers l’action. Il s’agit de « rassembler les éléments d’une méthode d’investigation et d’action après un suicide, lorsque l’on suspecte que le rapport au travail est en cause dans le chemin qui a conduit au geste fatal. » Dans cette perspective, trois ch..