Rahim Mahmoudvand (Bu-Ali Sina University and University of Cagliari)
Time Series with Multiple Observations per Period and Its Applications to Loss Ratio Data abstract
Abstract:
Time series with a single observation per period are commonly studied in the field of time series analysis. However, advancements in data recording technology have enabled the collection of time series with multiple observations per period. In the context of the insurance industry, for instance, we can consider claims within a period and compute loss ratios by dividing each claim by its corresponding premium. This approach results in a time series with multiple observations per period. In this talk, I will discuss methods for analyzing such datasets. Specifically, I will explore the application of both parametric and non-parametric approaches, combined with multivariate singular spectrum analysis, to produce forecasts for future observations.
11:00 • EPF Lausanne, Extranef 125
Adrien Laurent (INRIA Rennes)
Stochastic frozen-flow methods for the intrinsic integration of stochastic dynamics on Riemannian manifolds abstract
Abstract:
In stochastic optimization, molecular dynamics, quantum physics, or in the training of neural networks, one is often interested in sampling from the law of a stochastic process. These dynamics are often subject to geometric constraints (fixed distance between particles, Physics Informed Neural Networks, ...). In this context, it is crucial to develop numerical approaches that take into account both the geometric and random features of the dynamics. The literature uses penalty formulations or extrinsic numerical integrators. These solutions are costly, subject to significant time-step restrictions, and require formulation of the dynamics in much higher-dimensional spaces.In this talk, we present a new class of methods that rely on intrinsic geometric operations (in the spirit of Crouch-Grossman methods), a new robust convergence analysis, and an algebraic formalism of planar exotic Butcher series for the foundation of the weak order theory of intrinsic stochastic methods. A second order integrator is presented and tested numerically for a handful of manifolds.This is joint work with Eugen Bronasco and Baptiste Huguet.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05