Suppose a decision maker (DM) has partial information about certain events of a ?-algebra A belonging to set ? 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...

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 ?-compact topological space ?. The first part characterizes the strong and weak impatience in the context of discrete and continuous time flows of income (consumption) valued through a...

Considering that a natural way of sharing risks in insurance companies is to require risk by risk Pareto optimality, we offer in case of strong risk aversion, a simple computable method for deriving all Pareto optima. More importantly all Individually Rational Pareto optima can be computed...

Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting. Estimating the Tail Value-at-Risk for large portfolios or pricing basket...

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...

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...

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 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...