Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Population & Approximation algorithm. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Learning conditionally lexicographic preference relations

Abstract: We consider the problem of learning a user's ordinal preferences on a multiattribute domain, assuming that her preferences are lexicographic. We introduce a general graphical representation called LP-trees which captures various natural classes of such preference relations, depending on whether the importance order between attributes and/or the local preferences on the domain of each attribute is conditional on the values of other attributes. For each class we determine the Vapnik-Chernovenkis dimension, the communication complexity of preference elicitation, and the complexity of identifying a model in the class consistent with a set of user-provided examples.

Approximate Bayesian computation with the Wasserstein distance

Abstract: A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Levy‐driven stochastic volatility model.

Heterogeneous Beliefs and Asset Pricing in Discrete Time: An Analysis of Pessimism and Doubt

Abstract: The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete markets discrete time economy. The construction of a consensus belief, as well as a consensus consumer are shown to be valid modulo a predictable aggregation bias, which takes the form of a discount factor. We use our construction of a consensus consumer to investigate the impact of beliefs heterogeneity on the CCAPM and on the expression of the risk free rate. We focus on the pessimism/doubt of the consensus consumer and we study their impact on the equilibrium characteristics (market price of risk, risk free rate). We finally analyze how pessimism and doubt at the aggregate level result from pessimism and doubt at the individual level.