Stochastic modelling (insurance)

:This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset models. For mathematical definition, please see Stochastic process. "Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s). Its application initially started in physics. It is now being applied in engineering, life sciences, social sciences, and finance. See also Economic capital. Valuation Like any other company, an insurer has to show

Alternative(s) to fractional-diffusion equations in bedload transport models.

Christophe Ancey, Valentin Métraux, François Mettra

The idea of stochastic sediment transport models emerged in the 1930s, notably with the doctoral work of Hans A. Einstein (1936). Einstein's seminal work gave impulse to several stochastic models, which usually led to thin-tailed or bounded distributions for the particle-transport rate. Experimental observations together with field surveys suggest that particle-transport rate exhibits frequent and large fluctuations, in particular at low flow rates (i.e., when the bottom shear just exceeds the threshold of incipient motion), which cannot be described using classic distributions used so far for modelling bedload transport (e.g., Hamamori's distribution). The existence of these large and frequent fluctuations could offer a wide field of applications to fractional-derivative theory. Alternative approaches exist as well: in this talk, we explore the potentialities of a birth-death Markov model to model sediment transport within a fixed volume of control. Under steady-uniform-flow conditions, the model predicts that the number of moving particles inside the control volume follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy-tailed distributions, it may give rise to large and frequent fluctuations. We investigate the consequences of these fluctuations on bed dynamics, more especially on the features (growth rate and probability distribution) of nascent bedforms that develop on initially planar beds as a result of intermittent bedload transport.

2010

Microbial life in porous systems

David Scheidweiler

Microbial life in porous systems dominates the functioning of numerous ecosystems, ranging from stream sediments to soils. While these environments are characterized by structures that vary spatially over orders of magnitude, the traditional research focus has been on their macroscopic properties, such as porosity, permeability or pore connectivity. These approaches are effective in providing an overall description of the environment, but, they do not capture the impact of the spatial heterogeneity that is experienced by microorganisms. Such heterogeneity is assumed to play a major role on soil and sedimentary ecosystem functions, as well as being a driving force for selection and maintenance of microbial diversity. In order to cope with this heterogeneity microorganisms harness an arsenal of mechanisms to adapt to the prevailing conditions. They range from regulation of cell motility to modification of cell and colony morphology, production of matrix components, or generation of genetic and physiological heterogeneity. The present thesis focuses on the role of pore spatial heterogeneity and transport dynamics on microbial life in porous systems. The relevance of this thesis lies in the fact that it couples pore and near-cell scale physical mechanisms to the microbial processes at the larger landscape-scale. This multi-scale approach, obtained exploiting microfluidic experiments and time-lapse microscopy allowed me to investigate dispersal and space exploitation of microorganisms in porous systems. By means of a novel stochastic model, I combine measured pore scale trajectories of individual cells to the overall landscape transport. I show that motile cells of Pseudomonas putida disperse more efficiently, than non-motile cells, through a heterogeneous porous system. Motile cells can evade flow-imposed trajectories, enabling them to explore larger pore areas than non-motile cells. Additionally, motile cells are capable of reorienting their body towards flow direction, so increasing the population velocity and significantly impacting the overall transport properties. In case of a resident biofilm throughout the porous system, microbial transport exhibited preferential flow paths, and higher attachment rate. These two effects were more pronounced for non-motile than for motile cells. These findings suggest that motility couples with heterogeneous flows and that it can be beneficial to bacterial cells in confined environments as it enables them to actively explore space for resources or evade from regions with unfavorable conditions. In a second set of experiments, I studied the growth of a multispecies bacterial community in a porous system. Biofilms consistently differentiated into an annular base biofilm coating the grains and streamers protruding into the pore space. Different biophysical processes ruled this differentiation. While streamer growth dynamics is well explained by a filtration model, base biofilm expanded its radial growth by producing a tortuous surface, which enhances mass transfer. This architectural plasticity allowed the complementary use of the space provided by the grain-pore complexes, enhancing space exploitation at the larger scale of the porous system. Collectively, these findings unravel the biophysical underpinnings to the success of multispecies biofilms in porous environments.

EPFL2019

Microbial life in porous systems

David Scheidweiler

EPFL2019