Related papers: Risk Forms: Representation, Disintegration, and Ap…
This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail…
This paper investigates ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. We focus on joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
In this note, we determine, by a disjunctive normal form theorem, which functions on the standard $n$-nuanced \L ukasiewicz-Moisil algebra are representable by formulas and we show how this result may help in establishing the structure of…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
Given a real valued functional T on the space of bounded random variables, we investigate the problem of the existence of a conditional version of nonlinear means. We follow a seminal idea by Chisini (1929), defining a mean as the solution…
Models continue to increase their already broad use across industry as well as their sophistication. Worldwide regulation oblige financial institutions to manage and address model risk with the same severity as any other type of risk, which…
$W$-representation realizes partition functions by an action of a cut-and-join-like operator on the vacuum state with a zero-mode background. We provide explicit formulas of this kind for $\beta$- and $q,t$-deformations of the simplest…
We prove a generalisation of the disintegration theorem to the setting of multifunctions between Polish probability spaces. Whereas the classical disintegration theorem guarantees the disintegration of a probability measure along the…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
We present an elementary state augmentation method for a class of static risk measure applied to the total cost for both Markov decision processes and stochastic optimal control, such that dynamic programming equations can be derived on the…
Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase…
"What are the origins of risks?" and "How material are they?" -- these are the two most fundamental questions of any risk analysis. Quantitative Structuring -- a technology for building financial products -- provides economically meaningful…
We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement…
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…
In this paper, we study two classes of Kirchhoff type problems set on a double phase framework. That is, the functional space where finding solutions coincides with the Musielak-Orlicz-Sobolev space $W^{1,\mathcal H}_0(\Omega)$, with…