Finite time ruin probabilities with one Laplace inversion.

In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]—see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, 1981]—and it considers the deficit at ruin as wellFinite-time ruin probability; Phase-type distribution; Deficit at ruin; Lundberg’s equation; Laplace transform;

The Gerber-Shiu expected discounted penalty-reward function under an affine jump-diffusion model.

We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004)First passage problems; Risk process; Stochastic rates of interest; Ruin with interest; Affine jump-diffusion models; Penalty/reward functions at ruin;

The prevalence of high dysplastic colonic adenomatous polyps in a 3 year endoscopic retrospective study from a single clinical center

Introduction: Many colon neoplastic tumors come from the malignancy of adenomatous polyps (70%-90%) that were not timely diagnosed in order to be resected. Materials and Methods: We conducted a retrospective study regarding the incidence of adenomatous polyps during 1.000 consecutive colonoscopies performed in our Upper and Lower Digestive Endoscopy Laboratory during a three-year period. Results: During these colonoscopies, some targeted polyps were biopsied or completely removed and the samples had been sent to a complete anatomopathological examination. Taking into consideration the results, the polyps were classified after the histological type and the form of dysplasia, in order to determine the polyp forms that present a high risk of malignancy. Conclusion: Given the rather high frequency of malignant polyps discovered during our study, we highly recommend colonoscopy as a method of choice for routine monitoring of selected cases

On the valuation ofconstant barrier options under spectrally one-sided exponential L&evy models and Carr’s approximation for American puts.

This paper provides a general framework for pricing options with a constant barrier under spectrally one-sided exponential L&evy model, and uses it to implement ofCarr’s approximation for the value of the American put under this model. Simple analytic approximations for the exercise boundary and option value are obtained. c 2002 Elsevier Science B.V. All rights reservedAmerican options; Perpetual approximation; Spectrally negative exponential L&evy process;

Transport of polymer particles in a oil-water flow in porous media: enhancing oil recovery

We study a heuristic, core-scale model for the transport of polymer particles in a two phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. The recovery mechanism is believed to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels lead to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation for the polymer particles. A key aspect of the formulation is that the microscopic heterogeneity of the rock and a dynamic altering of the permeability must be taken into account in the rate equations.Comment: 20 pages, 9 Figures Submitted to Transport in Porous Medi

Well-posedness of the fully coupled quasi-static thermo-poro-elastic equations with nonlinear convective transport

This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists of a momentum balance equation, a mass balance equation, and an energy balance equation, fully coupled and nonlinear due to a convective transport term in the energy balance equation. The aim of this article is to investigate, in the context of mixed formulations, the existence and uniqueness of a weak solution to this model problem. The primary variables in these formulations are the fluid pressure, temperature and elastic displacement as well as the Darcy flux, heat flux and total stress. The well-posedness of a linearized formulation is addressed first through the use of a Galerkin method and suitable a priori estimates. This is used next to study the well-posedness of an iterative solution procedure for the full nonlinear problem. A convergence proof for this algorithm is then inferred by a contraction of successive difference functions of the iterates using suitable norms.Comment: 22 page