Endogeneity and Instrumental Variables in Dynamic Models

The objective of the paper is to draw the theory of endogeneity in dynamic models in discrete and continuous time, in particular for diffusions and counting processes. We first provide an extension of the separable set-up to a separable dynamic framework given in term of semi-martingale decomposition. Then we define our function of interest as a stopping time for an additional noise process, whose role is played by a Brownian motion for diffusions, and a Poisson process for counting processes.

Improved Complexity Bounds for Counting Points on Hyperelliptic Curves

We present a probabilistic Las Vegas algorithm for computing the local zeta function of a hyperelliptic curve of genus $g$ defined over $\mathbb{F}_q$. It is based on the approaches by Schoof and Pila combined with a modeling of the $\ell$-torsion by structured polynomial systems. Our main result improves on previously known complexity bounds by showing that there exists a constant $c>0$ such that, for any fixed $g$, this algorithm has expected time and space complexity $O((\log q)^{cg})$ as $q$ grows and the characteristic is large enough.Comment: To appear in Foundations of Computational Mathematic

Identifiability issues of age-period and age-period-cohort models of the Lee-Carter type

The predominant way of modelling mortality rates is the Lee-Carter model and its many extensions. The Lee-Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age-period or plug-in age-period-cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realisations, we investigate whether the expected values and covariances of the plug-in Lee-Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models

Nonparametric Analysis of Hedge Funds Lifetimes

Most of hedge funds databases are now keeping history of dead funds in order to control biases in empirical analysis. It is then possible to use these data for the analysis of hedge funds lifetimes and survivorship. This paper proposes two nonparametric specifications of duration models. First, the single risk model is an alternative to parametric duration models used in the literature. Second, the competing risks model consider the two reasons why hedge funds stop reporting. We apply the two models to hedge funds data and compare our results to the literature. In particular, we show that a cohort effect must be considered. Moreover, the reason of the exit is a crucial information for the analysis of funds' survival as for a large part of disappearing funds, exit cannot be explained by low performance or low level of assets.

Electromagnetic wave propagation and absorption in magnetised plasmas: variational formulations and domain decomposition

We consider a model for the propagation and absorption of electromagnetic waves (in the time-harmonic regime) in a magnetised plasma. We present a rigorous derivation of the model and several boundary conditions modelling wave injection into the plasma. Then we propose several variational formulations, mixed and non-mixed, and prove their well-posedness thanks to a theorem by S\'ebelin et~al. Finally, we propose a non-overlapping domain decomposition framework, show its well-posedness and equivalence with the one-domain formulation. These results appear strongly linked to the spectral properties of the plasma dielectric tensor

Polarization of stars with debris disks: comparing observations with models

The $Herschel$ Space telescope carried out an unprecedented survey of nearby stars for debris disks. The dust present in these debris disks scatters and polarizes stellar light in the visible part of the spectrum. We explore what can be learned with aperture polarimetry and detailed radiative transfer modelling about stellar systems with debris disks. We present a polarimetric survey, with measurements from the literature, of candidate stars observed by DEBRIS and DUNES $Herschel$ surveys. We perform a statistical analysis of the polarimetric data with the detection of far-infrared excess by $Herschel$ and $Spitzer$ with a sample of 223 stars. Monte Carlo simulations were performed to determine the effects of various model parameters on the polarization level and find the mass required for detection with current instruments. Eighteen stars were detected with a polarization $0.01 \le P \lesssim 0.1$ per cent and $\ge3\sigma_P$, but only two of them have a debris disk. No statistically significant difference is found between the different groups of stars, with, without, and unknown status for far-infrared excess, and presence of polarization. The simulations show that the integrated polarization is rather small, usually $< 0.01$ per cent for typical masses detected by their far-infrared excess for hot and most warm disks. Masses observed in cold disks can produce polarization levels above $0.01$ per cent since there is usually more dust in them than in closer disks. We list five factors which can explain the observed low-polarization detection rate. Observations with high-precision polarimeters should lead to additional constraints on models of unresolved debris disks.Comment: Corrected some quotations and typos and deleted superfluous references. 20 pages, 5 figure