Related papers: Ordering and Inequalities for Mixtures on Risk Agg…

This paper focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and…

In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…

We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic…

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with…

Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…

Researchers often have to deal with heterogeneous population with mixed regression relationships, increasingly so in the era of data explosion. In such problems, when there are many candidate predictors, it is not only of interest to…

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

Several interesting models for contingency tables are defined by a system of equality and inequality constraints on a suitable set of marginal log-linear parameters. After reviewing the most common difficulties which are intrinsic to order…

This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the…

We develop a nonparametric Bayesian modeling framework for clustered ordinal responses in developmental toxicity studies, which typically exhibit extensive heterogeneity. The primary focus of these studies is to examine the dose-response…

Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been…

Calibration and uncertainty estimation are crucial topics in high-risk environments. We introduce a new diversity regularizer for classification tasks that uses out-of-distribution samples and increases the overall accuracy, calibration and…

Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…

Several real-world systems can be represented as multi-layer complex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical…

We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggregate" and "first aggregate, then allocate" type. In both…

In this paper, we address risk aggregation and capital allocation problems in the presence of dependence between risks. The dependence structure is defined by a mixed Bernstein copula which represents a generalization of the well-known…

We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…