Alexis Bienvenüe

Niching in Monte Carlo Filtering Algorithms

Nonlinear multimodal filtering problems are usually addressed via Monte Carlo algorithms. These algorithms involve sampling procedures that are similar to proportional selection in genetic algorithms, and that are prone to failure due to genetic drift. This work investigates the feasibility and the relevance of niching strategies in this context. Sharing methods are evaluated experimentally, and prove to be efficient in such issues.

On hyperbolic iterated distortions for the adjustment of survival functions

This paper presents a class of distortions of survival functions. Studied distortions are built in order to respect several properties that seem to us useful in actuarial science. We focus here on some particular hyperbolic distortions, which preserve analytic invertibility of the distorted survival function, and for which inverse distortions belong to the same hyperbolic class. We propose some specific parameterizations of these distortions which give a straightforward inversion, and discuss the importance of such an inversion in insurance and finance. We prove the convergence of composed distortions to any target law, and give initial values and a particular methodology for the parameters estimation. Numerical figures illustrate the adaptation of these distortions to several actuarial fields.

Convergence of a Genetic Algorithm with finite population

We study the asymptotic behaviour of a mutation-selection genetic algorithm on the integers with finite population, defined by a simple random walk and the fitness function f (x) = x. We prove the convergence in law of the normalized population and a large deviations principle.