Related papers: Monetary value measures in a category of probabili…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
We will characterise robust monetary utility functions defined on the space of real valued (bounded) continuous functions on a Polish space.
A program for categorifying measure theory is outlined.
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.
Data valuation has become an increasingly significant discipline in data science due to the economic value of data. In the context of machine learning (ML), data valuation methods aim to equitably measure the contribution of each data point…
The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $\pi_{\mathfrak p}$ from [22].
Working within enriched category theory, we further develop the use of soundness, introduced by Ad\'amek, Borceux, Lack, and Rosick\'y for ordinary categories. In particular we investigate: (1) the theory of locally $\Phi$-presentable…
I review recent progress in defining probability distributions in the inflationary multiverse.
We develop integration theory for integrating functions taking values into a Dedekind complete unital $f$-algebra $\mathbb{L}$ with respect to $\mathbb{L}$-valued measures. We then discuss and prove completeness results of…
We construct a factorization of the Giry monad through the category of convex spaces, and show that, provided that no measurable cardinals exist, probability measures can be viewed as natural transformations. Using the adjunction of this…
In this manuscript, we define and study probabilistic values for cooperative games on simplicial complexes. Inspired by the work of Weber "Probabilistic values for games", we establish the new theory step by step, following the classical…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
Starting from the global financial crisis to the more recent disruptions brought about by geopolitical tensions and public health crises, the volatility of risk in financial markets has increased significantly. This underscores the…
We aim to contribute to the literature on product space and diversification by proposing a number of extensions of the current literature: (1) we propose that the alternative but related idea of a country space also has empirical and…
Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim…
This paper is a follow-up to the author's work "Topology of probability measure space, I" devoted to investigation of the functors $\hat P$ and $P_\tau$ of spaces of probability $\tau$-smooth and Radon measures. In this part, we study the…
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.