This chapter of a collective book aims at presenting the basics of decision making under risk. We first define notions of risk and increasing risk and recall definitions and classifications (that are valid independently of any representation) of behavior under risk. We then review the classical...

The aim of this paper is two-fold : first, to emphasize that the seminal result of Dow and Werlang [7] remains valid under weaker conditions, and this even if non-positive prices are considered, or equally that the no-trade interval result is robust when considering assets which can yield...

This paper is concerned with real valued set functions defined on the set of Borel sets of a locally compact σ-compact topological space Ω. The first part characterizes the strong and weak impatience in the context of discrete and continuous time flows of income (consumption) valued through a...

This chapiter of a collective book is dedicated to classical decision models under uncertainty, i.e. under situations where events do not have "objective" probabilities with which the Decision Marker agrees. We present successively the two main theories, their axiomatic, the interpretation and...

This chapter of a collective book aims at presenting cardinal extensions of the EU model, based on the Choquet integral, which allow to take into account observed behaviors as in Allais' paradox under risk or Ellsberg's paradox under uncertainty, where the expected utility model is violated....

This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in...

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.

The aim of this paper is two-fold : first, to emphasize that the seminal result of Dow and Werlang [9] remains valid under weaker conditions and this even if non-positive prices are considered, or equally that the no-trade interval result is robust when considering assets which can yield...

Suppose a decision maker (DM) has partial information about certain events of a σ-algebra A belonging to set ε and assesses their likelihood through a capacity v. When is this information probabilistic, i.e. compatible with a probability ? We consider three notions of compatibility with a...

We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the...