A tree approach to pp-variation and to integration

We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of $p$-variation of the path, and integration with respect to the path. In particular, the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths theory, are written as integrals on the tree. Examples include some stochastic paths such as martingales, L\'evy processes and fractional Brownian motions (for which an estimator of the Hurst parameter is given)

Representation formulae for the fractional Brownian motion

We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients. The basic notions of fractional calculus which are needed for the study are introduced. As an application, we also prove some properties of the Cameron-Martin space of the fractional Brownian motion, and compare its law with the law of some of its variants. Several of the results which are given here are not new; our aim is to provide a unified treatment of some previous literature, and to give alternative proofs and additional results; we also try to be as self-contained as possible.Comment: to appear in "S\'eminaire de Probabilit\'es

Optimal risk financing in large corporations through insurance captives

A captive is an insurance or reinsurance company established by a parent group to finance its own risks. Captives mix internal risk pooling between the business units of the parent group and risk transfer toward the reinsurance market. We analyze captives from an optimal insurance contract perspective. The paper considers the vertical contractual chain that links firstly business units to insurance captives or to "fronters" through insurance contracts, secondly fronters to reinsurance captives through the cession of risks and thirdly insurance or reinsurance captives to reinsurers through cessions or retrocessions. In particular, the risk cession by fronters to a reinsurance captive trades o¤ the benefits derived from recouped premiums and from the risk sharing advantage of an "umbrella reinsurance policy", against the risks that result from the captive liabilities. The optimal captive scheme depends on the price of coverage in insurance and reinsurance markets and on the parent group's corporate capital. Since these variables fluctuate across time, the analysis developed in this paper corroborates the intertemporal variability of captives activity.self-insurance, captive, reinsurance, risk management

Point-record driving licence and road safety : an economic approach

Les permis de conduire à points sont aujourd'hui très largement utilisés pour faire respecter les politiques de sécurité routière, avec toutefois des mises en oeuvre diverses selon les pays et parfois à l'intérieur d'un même pays. Comme toute sanction non-monétaire, priver les contrevenants de leur permis permet aux autorités publiques de retirer de la route les individus dangereux et aussi de dissuader les conducteurs normaux d'enfreindre le code de la route. Nous analysons les caractéristiques souhaitables des mécanismes de permis à points et, en particulier, nous étudions s'ils devraient inclure des clauses de récupération des points perdus et des périodes probatoires. Nous envisageons également la possibilité d'un retrait immédiat du permis de conduire pour les infractions les plus graves.

Mass transfer in a membrane aerated biofilm

We present experimental results of mass transfer of a non reactive tracer gas (neon)measured in aerobic heterotrophic biofilm developed from activated sludge. Biofilms are grown in various hydrodynamic conditions and the effective diffusivity is used to quantify the mass transfer through the biofilm. Beyond some cross-flow conditions, the effective diffusivity through the biofilm seems larger than in the bulk. This can be explained by a dispersion generated by convection inside the biofilm, as supported by an analytical flow model and in accordance to the numerical simulation proposed by Aspa et al. (2011)