Related papers: On expected and von Neumann-Morgenstern utility fu…
Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty…
We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous…
Let $\succsim$ be a binary relation on the set of simple lotteries over a countable outcome set $Z$. We provide necessary and sufficient conditions on $\succsim$ to guarantee the existence of a set $U$ of von Neumann--Morgenstern utility…
The von Neumann-Morgenstern (VNM) utility theorem shows that under certain axioms of rationality, decision-making is reduced to maximizing the expectation of some utility function. We extend these axioms to increasingly structured…
The use of von Neumann -- Morgenstern utility is examined in the context of multiple choices between lotteries. Different conclusions are reached if the choices are simultaneous or sequential. It is demonstrated that utility cannot be…
In this paper, we study the continuity of expected utility functions, and derive a necessary and sufficient condition for a weak order on the space of simple probabilities to have a continuous expected utility function. We also verify that…
In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and…
A model for decision making that generalizes Expected Utility Maximization is presented. This model, Expected Qualitative Utility Maximization, encompasses the Maximin criterion. It relaxes both the Independence and the Continuity…
This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity,…
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…
We obtain variants of the classical von Neumann-Morgenstern expected utility theorem, with and without the completeness axiom, in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary…
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,…
We present a necessary and sufficient condition for Alt's system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can…
The total loss function associated with a set of cross-sectional predictions, that is, estimates or forecasts, summarizes the set's overall accuracy. Its arguments are the individual cross-sectional units' loss functions. Under general…
In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\'an…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable…
The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…