Related papers: The Algebra of Utility Inference
This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages…
We examine behavioral axioms in decision theory that are satisfied approximately rather than exactly. We demonstrate that in key domains -- decisions under risk, uncertainty, and intertemporal choice -- behavior that \emph{almost} satisfies…
We propose an axiomatic approach which economically underpins the representation of dynamic preferences in terms of a stochastic utility function, sensitive to the information available to the decision maker. Our construction is iterative…
We obtain a full characterization of consistency with respect to higher-order stochastic dominance within the rank-dependent utility model. Different from the results in the literature, we do not assume any condition on the utility…
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 short paper we introduce a new class of performance measures based on certainty equivalents defined via scaled utility functions. We analyse their properties, show that the corresponding portfolio optimization problem is well-posed…
In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision…
This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…
Whether the goal is to analyze voting behavior, locate facilities, or recommend products, the problem of translating between (ordinal) rankings and (numerical) utilities arises naturally in many contexts. This task is commonly approached by…
Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which…
Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial intelligence. To help reduce the conflict between these two approaches,…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
We introduce an axiomatization for the notion of computation. Based on the idea of Brouwer choice sequences, we construct a model, denoted by $E$, which satisfies our axioms and $E \models \mathrm{ P \neq NP}$. In other words, regarding…
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…
We propose and develop an algebraic approach to revealed preference. Our approach dispenses with non algebraic structure, such as topological assumptions. We provide algebraic axioms of revealed preference that subsume previous, classical…
Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple…
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of…
We consider a model for decision making based on an adaptive, k-period, learning process where the priors are selected according to Von Neumann-Morgenstern expected utility principle. A preference relation between two prospects is…
Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of…
Budget aggregation is a process in which citizens vote by declaring their individual ideal budget allocation, and a pre-determined rule aggregates all votes into a single outcome. Recent theoretical work has proposed various aggregation…