arXiv subjects

Alessandro Mutti

Publications and source records attributed to Alessandro Mutti.

5 recordsLinked to original sources

arXiv2026

Conway--Maxwell multivariate Bernoulli distribution

We investigate the Conway--Maxwell multivariate Bernoulli distributions, a family of multivariate Bernoulli distributions derived from the Conway--Maxwell-binomial distribution. We show that it is possible to set the parametrization such that the Bernoulli marginals remain intact, allowing us to study dependence properties within this family. In particular, we demonstrate that this family spans the full spectrum of dependence. Moreover, for specific ranges of the parameters, these distributions satisfy the strongly Rayleigh property, a negative dependence notion stronger than negative association.

math.ST↗

arXiv2025

Additive subordination of multiparameter Markov processes

In this work, we consider, in a general setting, multiparameter multidimensional Markov processes that are time-changed by an independent additive subordinator. By extending Phillips theorem, we show that the resulting process is a Feller evolution and we characterize its generator. We further derive its pseudo-differential representation and show that its symbol admits a L\'evy-Khintchine representation. In the specific case of multiparameter Ornstein-Uhlenbeck processes, we obtain explicit expression of the symbol, along with the associated characteristic L\'evy triplet. As an application, we consider a factor-based specification for the Ornstein-Uhlenbeck process subordinated by a Sato process. The constructive nature of this process is inspired by applications in finance.

math.PR↗

arXiv2025

Extremal negative dependence and the strongly Rayleigh property

We provide a geometrical characterization of extremal negative dependence as a convex polytope in the simplex of multidimensional Bernoulli distributions, and we prove that it is an antichain that satisfies some minimality conditions with respect to the strongest negative dependence orders. We study the strongly Rayleigh property within this class and explicitly find a distribution that satisfies this property by maximizing the entropy. Furthermore, we construct a chain for the supermodular order starting from extremal negative dependence to independence by mixing the maximum entropy strongly Rayleigh distribution with independence.

math.PR↗

arXiv2024

Generalized FGM dependence: Geometrical representation and convex bounds on sums

Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find sharp bounds in this class for many aggregate risk measures, such as value-at-risk, expected shortfall, and entropic risk measure, by enumerating their values on the extremal points of the convex polytope. This is infeasible in high dimensions. We overcome this limitation by considering the aggregation of identically distributed risks with generalized FGM copula specified by a common parameter $p$. In this case, the analogy with the geometrical structure of the class of Bernoulli distribution allows us to provide sharp analytical bounds for convex risk measures.

q-fin.MF↗

arXiv2023

Symmetric Bernoulli distributions and minimal dependence copulas

The key result of this paper is to characterize all the multivariate symmetric Bernoulli distributions whose sum is minimal under convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli random vectors, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas corresponding to symmetric Bernoulli random vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties.

math.ST↗