A Discrete Choquet Integral for Ordered Systems

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical non-negative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on the set system. It is shown that the general Choquet integral can be computed by a simple Monge-type algorithm for so-called intersection systems, which include as a special case weakly union-closed families. Generalizing Lov\'asz' classical characterization, we give a characterization of the superadditivity of the Choquet integral relative to a capacity on a union-closed system in terms of an appropriate model of supermodularity of such capacities

A Discrete Choquet Integral for Ordered Systems

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical non-negative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on the set system. It is shown that the general Choquet integral can be computed by a simple Monge-type algorithm for so-called intersection systems, which include as a special case weakly union-closed families. Generalizing Lovász' classical characterization, we give a characterization of the superadditivity of the Choquet integral relative to a capacity on a union-closed system in terms of an appropriate model of supermodularity of such capacities.Choquet integral, belief function, measurability, set systems, Monge algorithm, supermodularity

In search of characterization of the preference for safety under the Choquet model

Victor prefers safety more than Ursula if whenever Ursula prefers some constant to some uncertain act, so does Victor. This paradigm, whose Expected Utility version takes the form of Arrow & Pratt's more risk averse concept, will be studied in the Choquet Uncertainty model, letting u and μ (v and ν) be Ursula's (Victor's) utility and capacity. A necessary and sufficient condition (A) on the pairs (u, μ) and (v, ν) will be presented for dichotomous weak increased uncertainty aversion, the preference by Victor of a constant over a dichotomous act whenever such is the preference of Ursula. This condition, pointwise inequality between a function defined in terms of v (u-1(⋅)) and another defined purely in terms of the capacities, preserves the flavor of the "more pessimism than greediness" characterization of monotone risk aversion by Chateauneuf, Cohen & Meilijson in the Rank-dependent Utility Model and its extension by Grant & Quiggin to the Choquet Utility Model. A sufficient condition (B) in terms of the capacities only, satisfied in particular if ν (⋅) = f (μ (⋅)) for some convex f, will be presented for more simplicity seeking, the preference by Victor over any act for some dichotomous act, that leaves Ursula indifferent. Condition A is thus a characterization of weak increased uncertainty aversion for convex f. An example will be exhibited disproving the more far reaching conjecture under which the dichotomous case implies the general case.Choquet Utility, greediness, pessimism, Rank-dependent Utility, Risk aversion, uncertainty.

More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model

This paper studies monotone risk aversion, the aversion to monotone, meanpreserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by twofunctions, a utility function u in conjunction with a probability-perception function f.Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel & Lehmann [3, 4] in Non-parametric Statistics. We present a characterization of the pairs (u; f) of monotone risk averse decision makers, based on an index of greediness Gu of the utility function u and an index of pessimism Pf of the probability perception function f: the decision maker is monotone risk averse if and onlyif Pf exceeds Gu. A novel element is that concavity of u is not necessary. In fact, u must be concave only if Pf = 1.Risk aversion, pessimism, greediness, Rank-dependent Expected Utility

Modeling attitudes toward uncertainty through the use of the Sugeno integral

The aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion.Sugeno integral; uncertainty aversion; preference relations; ordinal information

Modeling attitudes toward uncertainty through the use of the Sugeno integral

International audienceThe aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion

A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.multicriteria decision making; Choquet integral; 2-additive capacity; MACBETH

Analysis of decision-making in ambiguous economic and market evidences

至今，人们已普遍意识到Knight不确定性的概念比风险更加贴近现实，并且与风险情形下决策行为有很大的不同，当前该领域的大部分研究都集中在奈特不确定情形下决策理论及其应用，本文的目的在于梳理已有的有关模糊(Ambigulity)经济的决策理论模型的同时，完善模糊经济中的决策理论的公理化体系，刻画模糊厌恶、不确定性厌恶、模糊溢价、不确定性溢价，以及定价模型和风险管理模型等问题。在模糊经济框架下，基于KMM模型，给出双期望效用的表示形式，并建立了比较模糊厌恶的框架，给出了模糊态度和模糊信念的刻画，在此基础之上，导出了模糊经济框架下的不确定性溢价由纯风险溢价和模糊溢价构成，推导出了不确定性溢价、模糊溢...So far, it has been generally kown tnat the Knight uncertainty is closer to reality than the risk, and decision-making behavior and risk situations are very different between them. Most of the studies in this field are concentrated in the Knight uncertain circumstances, decision theory and its application. The purpose of this paper is to comb the already Ambiguity theoretical models of economic de...学位：博士后院系专业：经济学院金融系_金融工程学号：200917002

Representation of maxitive measures: an overview

Idempotent integration is an analogue of Lebesgue integration where $\sigma$-maxitive measures replace $\sigma$-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent integral, we also prove new results of the same kind.Comment: 40 page