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A well-designed framework for risk classification and ratemaking in automobile insurance is key to insurers' profitability and risk management, while also ensuring that policyholders are charged a fair premium according to their risk…
We define and study multivariate exponential functions, symmetric with respect to the alternating group A_n, which is a subgroup of the permutation (symmetric) group S_n. These functions are connected with multivariate exponential…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras $\cl(Q)$ to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in $\cl(Q),$…
In linear regression modelling the distortion of effects after marginalizing over variables of the conditioning set has been widely studied in several contexts. For Gaussian variables, the relationship between marginal and partial…
We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon…
A new method of analysing positive bistochastic maps on the algebra of complex matrices $M_{3}$ has been proposed. By identifying the set of such maps with a convex set of linear operators on $\mathbb{R}^{8}$, one can employ techniques from…
In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…
Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov's multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Handling outliers is a fundamental challenge in multivariate data analysis because outliers may distort the structures of correlation or conditional independence. Although robust Bayesian inference has been extensively studied in univariate…
We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…
There is an abundance of useful fluctuation identities for one-sided L\'evy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix…
The paper studies conical, convex, and affine models in the framework of behavioral systems theory. We investigate basic properties of such behaviors and address the problem of constructing models from measured data. We prove that closed,…
Risk management is an important part of financial practice, essential for protecting assets and investments in modern-day volatile markets. This paper proposes a mixture of mirrored Weibull (MMW) distribution for modelling stock returns and…