We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of...

We formulate a new theory of expected utility under uncertainty based on the notion of an event-lattice, which is a natural generalization of a Savage state space. The modelling of uncertainty is based on the idea that the decision maker for each group of related decisions to be taken creates a...

We model the notion of a "small world" as a context dependent state space embedded into the "grand world". For each situation the decision maker creates a "small world" reflecting the events perceived to be relevant for the act under consideration. The "grand world" is represented by an event...

We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of...

The operator convex functions of several variables are characterized in terms of a non-commutative generalization of Jensen's inequality, extending previous results of F. Hansen and G.K. Pedersen for functions of one variable and of F. Hansen for functions of two variables.

We consider the risk premium demanded by a decision maker with wealth x in order to be indifferent between obtaining a new level of wealth y1 with certainty, or to participate in a lottery which either results in unchanged present wealth or a level of wealth y2 y1. We define the relative risk...

We formulate a new theory of expected utility under uncertainty based on the notion of an event-lattice, which is a natural generalization of a Savage state space. The modelling of uncertainty is based on the idea that the decision maker for each group of related decisions to be taken creates a...

Functions mapping the set of symmetric matrices with non-negative entries into itself are monotonous with respect to the associated order structure. Such functions are analytic and the derivatives in zero of arbitrary order are non-negative.