Related papers: Probability Premium and Attitude Towards Probabili…
We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…
Social scientists have long sought to understand why certain people, items, or options become more popular than others. One seemingly intuitive theory is that inherent value drives popularity. An alternative theory claims that popularity is…
The probability of necessity (PN), which quantifies the probability that an observed event would not have occurred in the absence of the treatment, is a central estimand in attribution analysis. While PN has been extensively studied for…
In this paper an interesting application of mathematics in economics is presented: the formulation of the theory of consumer basic problem, grounded on the concept of preferences relation and operationalized with optimization tools.
In this paper, we establish a mathematical duality between utility transforms and probability distortions. These transforms play a central role in decision under risk by forming the foundation for the classic theories of expected utility,…
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
Reputation is generally defined as the opinion of a group on an aspect of a thing. This paper presents a reputation model that follows a probabilistic modelling of opinions based on three main concepts: (1) the value of an opinion decays…
We provide an axiomatic approach to general premium principles in a probability-free setting that allows for Knightian uncertainty. Every premium principle is the sum of a risk measure, as a generalization of the expected value, and a…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
McFadden and Richter (1991) and later McFadden (2005) show that the Axiom of Revealed Stochastic Preference characterizes rationalizability of choice probabilities through random utility models on finite universal choice spaces. This note…
Rate change calculations in the literature involve deterministic methods that measure the change in premium for a given policy. The definition of rate change as a statistical parameter is proposed to address the stochastic nature of the…
This paper proposes two mixed models to study a consumer's optimal saving in the presence of two types of risk.
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming, called probability answer set optimization programs. The proposed…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
This study provides the solution to the equity premium puzzle. The new model was developed by including the behavior of investors toward risk in financial markets in prior studies. The calculations of this newly tested model show that the…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…