102 research outputs found
Multi-group Binary Choice with Social Interaction and a Random Communication Structure -- a Random Graph Approach
We construct and analyze a random graph model for discrete choice with social
interaction and several groups of equal size. We concentrate on the case of two
groups of equal sizes and we allow the interaction strength within a group to
differ from the interaction strength between the two groups. Given that the
resulting graph is sufficiently dense we show that, with probability one, the
average decision in each of the two groups is the same as in the fully
connected model. In particular, we show that there is a phase transition: If
the interaction among a group and between the groups is strong enough the
average decision per group will either be positive or negative and the decision
of the two groups will be correlated. We also compute the free energy per
particle in our model
A Comparative Study of Sparse Associative Memories
We study various models of associative memories with sparse information, i.e.
a pattern to be stored is a random string of s and s with about
s, only. We compare different synaptic weights, architectures and retrieval
mechanisms to shed light on the influence of the various parameters on the
storage capacity.Comment: 28 pages, 2 figure
Measuring and Mitigating Biases in Motor Insurance Pricing
The non-life insurance sector operates within a highly competitive and
tightly regulated framework, confronting a pivotal juncture in the formulation
of pricing strategies. Insurers are compelled to harness a range of statistical
methodologies and available data to construct optimal pricing structures that
align with the overarching corporate strategy while accommodating the dynamics
of market competition. Given the fundamental societal role played by insurance,
premium rates are subject to rigorous scrutiny by regulatory authorities. These
rates must conform to principles of transparency, explainability, and ethical
considerations. Consequently, the act of pricing transcends mere statistical
calculations and carries the weight of strategic and societal factors. These
multifaceted concerns may drive insurers to establish equitable premiums,
taking into account various variables. For instance, regulations mandate the
provision of equitable premiums, considering factors such as policyholder
gender or mutualist group dynamics in accordance with respective corporate
strategies. Age-based premium fairness is also mandated. In certain insurance
domains, variables such as the presence of serious illnesses or disabilities
are emerging as new dimensions for evaluating fairness. Regardless of the
motivating factor prompting an insurer to adopt fairer pricing strategies for a
specific variable, the insurer must possess the capability to define, measure,
and ultimately mitigate any ethical biases inherent in its pricing practices
while upholding standards of consistency and performance. This study seeks to
provide a comprehensive set of tools for these endeavors and assess their
effectiveness through practical application in the context of automobile
insurance.Comment: 37 page
Time-changed normalizing flows for accurate SDE modeling
The generative paradigm has become increasingly important in machine learning
and deep learning models. Among popular generative models are normalizing
flows, which enable exact likelihood estimation by transforming a base
distribution through diffeomorphic transformations. Extending the normalizing
flow framework to handle time-indexed flows gave dynamic normalizing flows, a
powerful tool to model time series, stochastic processes, and neural stochastic
differential equations (SDEs). In this work, we propose a novel variant of
dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on
time deformation of a Brownian motion which constitutes a versatile and
extensive family of Gaussian processes. This approach enables us to effectively
model some SDEs, that cannot be modeled otherwise, including standard ones such
as the well-known Ornstein-Uhlenbeck process, and generalizes prior
methodologies, leading to improved results and better inference and prediction
capability
Collaborative Insurance Sustainability and Network Structure
The peer-to-peer (P2P) economy has been growing with the advent of the
Internet, with well known brands such as Uber or Airbnb being examples thereof.
In the insurance sector the approach is still in its infancy, but some
companies have started to explore P2P-based collaborative insurance products
(eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only
recently started to consider those risk sharing mechanisms, as in Denuit and
Robert (2021) or Feng et al. (2021). In this paper, describe and analyse such a
P2P product, with some reciprocal risk sharing contracts. Here, we consider the
case where policyholders still have an insurance contract, but the first
self-insurance layer, below the deductible, can be shared with friends. We
study the impact of the shape of the network (through the distribution of
degrees) on the risk reduction. We consider also some optimal setting of the
reciprocal commitments, and discuss the introduction of contracts with friends
of friends to mitigate some possible drawbacks of having people without enough
connections to exchange risks
Diffraction d'une onde acoustique (ou électromagnétique) par un plateau rigide (ou parfaitement conducteur)
National audienceL'objectif des travaux brièvement présentés dans ce papier était d'implémenter au sein de deux logiciels considérant la propagation en 3D d'ondes acoustiques et électromagnétiques à lancer de faisceaux (ICARE **) et tracé de rayons (CRT *) un modèle asymptotique (TUD) permettant de prendre en compte les phénomènes de double diffraction par un écran d'épaisseur donnée. Nous l'avons ensuite mis en œuvre dans différentes configurations afin d'en étudier le comportement. La dernière étape de ce travail a consisté à valider la formulation choisie en comparéléments finis de frontière (B.E.M) [JEA
Using asymptotic methods to compute diffracted pressure by curved surfaces
13 pagesInternational audienceThis article presents an original and efficient method to compute acoustic pressure diffracted by curved surfaces. Our approach is perfectly suited to be integrated into ray of beam tracing softwares
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