We discuss the role of ambiguity in randomized reinsurance contracts, focusing on one-period stop-loss treaties. Ambiguity is modeled as an ε-contamination of a reference joint probability with respect to the class of all finitely additive joint probabilities with a fixed loss marginal distribution. In a risk management perspective, we consider an insurer that systematically adopts a pessimistic attitude towards ambiguity. This translates in computing a lower expected profit, as a Choquet integral, and in adopting an ambiguous formulation of Value-at-Risk, both determined by the lower envelope of the ε-contamination class. Next, the optimal retention level is obtained by maximizing the insurer’s lower expected profit, that is by applying a maximin criterion of choice. We provide a complete characterization of a randomized stop-loss reinsurance contract under ambiguity, and we study the impact of the ambiguity parameter ε on the optimal retention level as well as on the resulting expected profit. Finally, we highlight the existence of an ambiguity threshold above which the benefit of randomization vanishes.

We focus on the marginal problem by relaxing the requirement of completely specified marginal probabilities, and referring to Dempster-Shafer theory to encode such partial probabilistic information. We investigate the structure of a suitable set of bivariate joint belief functions having fixed marginals by relying on copula theory. The chosen set of joint belief functions is used to minimize a functional of a given cost function, so as to select an optimal imprecise transport plan in the form of a joint belief function. We formulate two Kantorovich-like optimal transport problems by seeking to minimize the Choquet integral of the cost function with respect to either the reference set of joint belief functions or their dual plausibility functions. We give a noticeable application by choosing a metric as cost function: this permits to define pessimistic and optimistic Choquet-Wasserstein pseudo-distances, that can be used to compare belief functions on the same space. We finally deal with the problem of approximating a belief function with an element of a distinguished class of belief functions, by minimizing one of the two Choquet-Wasserstein pseudo-distances.

We address a multi-class classification problem on a tabular dataset comprising both continuous and categorical features, as commonly found in financial and actuarial domains. To achieve robust and reliable predictions, we propose a credal classifier built from an ensemble of augmented probabilistic models, each capable of self-assessing its confidence in the predicted class distribution for a given instance. Each base learner in the ensemble is implemented as a Confidence-Aware TabTransformer: a neural architecture that combines a sequence of transformer layers to process categorical variables, followed by a multi-layer perceptron for classification. In parallel, a dedicated confidence head outputs the model’s self-assessed reliability score. For ensemble aggregation, we explore multiple confidence-aware combination rules, applied after a [Formula: see text]-quantile filtering step to remove low-discordant outlier distribution. We demonstrate the effectiveness of this methodology on a fraud detection task, which is a representative binary classification problem with severe class imbalance.

The consequences of Dubois and Prade's minimum specificity principle are shown under a continuous t-norm T, when dealing with conditioning and independence in possibility theory. The minimum specificity principle singles out a particular sub-class of T-conditional possibilities (referred to as T-DP-conditional possibilities) adhering to a suitable axiomatic definition that relies on the residuum of T. Such a sub-class differentiates from the larger class of T-conditional possibilities in terms of non-closure with respect to pointwise limits, non-connectedness of extension sets, and Kolmogorov-like representation. We then switch to coherence for a partial assessment in both frameworks, highlighting that, under T-DP-conditioning, coherence of the global assessment cannot be characterized in terms of coherence on every finite sub-family. Finally, both for T-conditioning and T-DP-conditioning, we introduce an independence notion that implies logical independence and we investigate the differences due to minimum specificity.

The aim of the paper is to model ambiguity in a randomized reinsurance stop-loss treaty. For this, we consider the lower envelope of the set of bivariate joint probability distributions having a precise discrete marginal and an ambiguous Bernoulli marginal. Under an independence assumption, since the lower envelope fails 2-monotonicity, inner/outer Dempster-Shafer approximations are considered, so as to select the optimal retention level by maximizing the lower expected insurer's annual profit under reinsurance. We show that the inner approximation is not suitable in the reinsurance problem, while the outer approximation preserves the given marginal information, weaken the independence assumption, and does not introduce spurious information in the retention level selection problem. Finally, we provide a characterization of the optimal retention level.

We deal with conditional decomposable information measures, directly defined as functions on a suitable set of conditional events satisfying a class of axioms. For these general measures we introduce a notion of independence and study its main properties in order to compare it with classical definitions present in the literature. The particular case of Wiener-Shannon information measure is taken in consideration and the links between the provided independence for information measures and the independence for the underlying probability are analyzed.

In the literature there are different definitions of conditional possibility. Starting from a general axiomatic definition, we propose a definition of independence for ⊙-conditional possibility, in the case that ⊙ is a strictly monotone triangular norm. We study its main properties to compare it to other definitions introduced in possibility theory. Then, we show that the controversial aspects related to logical dependencies (structural zeros) can be circumvented. Moreover, a set of properties (the well-known graphoid properties) has been considered to be tested, allowing us to compare the proposed definition to the independence notions given in the context of other uncertainty formalisms. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 299–323, 2006.

In this paper we study conditional independence structures arising from conditional probabilities and lower conditional probabilities. Such models are based on notions of stochastic independence apt to manage also those situations where zero evaluations on possible events are present: this is particularly crucial for lower probability. The "graphoid" properties of such models are investigated, and the representation problem of conditional independence structures is dealt with by generalizing the wellknown classic separation criteria for undirected and directed acyclic graphs. Our graphical models describe the independence statements and the possible logical dependencies among the random variables.