arXiv subjects

Benjamin Côté

Publications and source records attributed to Benjamin Côté.

7 recordsLinked to original sources

arXiv2026

Tree-structured Ising models under mean parameterization

In the risk modeling literature, the Ising model has emerged as a valuable framework for dependent Bernoulli random variables, as its underlying graphical structure captures complex dependence patterns. It is almost always employed in its exponential-family parameterization, which comes with some drawbacks such as the marginal distributions not being fixed and an intractable normalizing constant. We study tree-structured Ising models under their mean parameterization, particularly well suited to risk modeling applications, especially as it eliminates these drawbacks. We study tree-structured Ising models under their mean parameterization, which eliminates these drawbacks and is particularly attractive for risk modeling. The mean parameterization also facilitates the characterization of dependence structures and the distribution of aggregate risks. In particular, we derive an analytic expression for the joint probability generating function, yielding an efficient method for computing the aggregate-risk distribution. Similarly, we obtain the ordinary generating function of expected allocations allowing exact computations for risk allocation. The mean parameterization also allows for a stochastic representation of Ising models, yielding a direct sampling algorithm otherwise unavailable under the exponential-family parameterization. We show that Markov random fields with fixed Poisson marginal distributions provide an efficient and accurate approximation for tree-structured Ising models, in the spirit of Poisson approximations.

math.ST↗

arXiv2026

Probability of worthwhile effect of monotone-response treatments

Experiments may, by design, prevent one from observing on a single subject both the response to a treatment and to its absence. Because of this, marginal distributions for both cases may be observable but not their joint distribution, thus obscuring the distribution of the treatment effect. We examine the case where we impose that the treatment effect is nonnegative, also called monotone treatment response, a common assumption relevant to many practical applications. We solve the problems of best- and worst-case probabilities that the treatment effect exceeds a given value, using an explicit construction for the dependence scheme in each case. Such problems can equivalently be described, in different contexts, as risk aggregation under dependence uncertainty and an order constraint, and as optimal transport with a particular cost function.

econ.EM↗

arXiv2026

On a risk model with tree-structured Poisson Markov random field frequency, with application to rainfall events

In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with Poisson marginals. The tree structure translates into a wide variety of dependence schemes. We study the global risk of the portfolio and the risk allocation to all its constituents. We provide asymptotic results for portfolios defined on infinitely growing trees. To illustrate its flexibility and computational scalability to higher dimensions, we calibrate the risk model on real-world extreme rainfall data and perform a risk analysis.

stat.ME↗

arXiv2026

On convex order and supermodular order without finite mean

Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex order by that of its comonotonic version and lower bounded by that of its counter-monotonic version, and all existing proofs of this result require the random variables' expectations to be finite. We show that the above result remains true even when discarding the finite-mean assumption, and obtain several other results on the comparison of infinite-mean random variables via the convex order. To our surprise, we find two deceivingly similar definitions of the convex order, both of which exist widely in the literature, and they are not equivalent for random variables with infinite mean. This subtle discrepancy in definitions also applies to the supermodular order, and it gives rise to some incorrect statements, often found in the literature.

math.PR↗

arXiv2025

Risk-insurance parity

Risk aversion and insurance are two prominent and interconnected concepts in economics and finance. To explore their fundamental connection, we introduce risk-insurance parity, which associates various classes of insurance contracts with different notions of risk aversion. We show that the classic notions -- both weak and strong -- of risk aversion can be characterized by propensity to different classes of insurance contracts, generalizing recent results on propensity to full, proportional, and deductible-limit contracts in the literature. We obtain full characterizations of the classes of insurance indemnity functions that correspond to weak and strong risk aversion. Risk-insurance parity allows us to define two new notions of risk aversion, between weak and strong, characterized by insurance propensity to deductible-only and limit-only contracts respectively.

econ.TH↗

arXiv2025

Centrality and shape-related comparisons in a tree-structured Markov random field

Understanding the effects of the choice of the tree on the joint distribution of a tree-structured Markov random field (MRF) is crucial for fully exploiting the intelligibility of such probabilistic graphical models. Tools must be developed in this regard: this is the overarching objective of this paper. Our discussion is two-fold. First, we examine concepts specific to network centrality theory. We put forth a new conception of centrality for MRFs that not only accounts for the tree topology, but also the underlying stochastic dynamics. In this vein, we compare synecdochic pairs, random vectors comprising a MRF's component and its sum, using stochastic orders. The resulting orderings are transferred to risk-allocation quantities, which therefore serve as new centrality indices tailored to our stochastic framework. Second, we shed light on the influence of the tree's shapes, by establishing convex orderings for MRFs encrypted on trees of different shapes. This results in the design of a new partial order on tree shapes. This analysis is done within the framework of a propagation-based family of tree-structured MRFs with the uncommon property of having fixed Poisson marginal distributions unaffected by the dependence scheme. This work is a first step into the analysis of MRFs' trees' shapes and a stepping stone to extending this analysis to a broader framework.

math.ST↗

arXiv2025

Tree-structured Markov random fields with Poisson marginal distributions

A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson with the same mean, and are untied from the strength or structure of their built-in dependence. This key feature is uncommon for Markov random fields and most convenient for applications purposes. The specific properties of this new family confer a straightforward sampling procedure and analytic expressions for the joint probability mass function and the joint probability generating function of the vector of counting random variables, thus granting computational methods that scale well to vectors of high dimension. We study the distribution of the sum of random variables constituting a Markov random field from the proposed family, analyze a random variable's individual contribution to that sum through expected allocations, and establish stochastic orderings to assess a wide understanding of their behavior.

stat.ME↗