The demonic product of two probabilistic relations is defined and investigated. It is shown that the product is stable under bisimulations when the mediating object is probabilistic, and that under some mild conditions the non-deterministic fringe of the probabilistic relations behaves properly: the fringe of the product equals the demonic product of the fringes.

Abstract. In this paper, we consider trading with proportional transaction costs as in [7]. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed, and show, in general, how to represent its closure in such a way that it is the cone of claims attainable for zero endowment, for a different set of trading prices. The new representation obeys the Fundamental Theorem of Asset Pricing. We then show how to represent claims and in a final section show how any such setup corresponds to a coherent risk measure.

Introduction A classical reference for the theory of random sets is [7]. Updated supplements are [11], [8], [1], and the references found therein. A random set F in a set X is described by assignment of a consistent probability to the hit event F T C 6= ; for every fixed set C in a suitable family of sets. If F and G are random sets it is natural to ask if the union F S G and intersection F T G also are random sets. Clearly the union F S G hits C iff F hits C or G hits C, so the union is a random set. Similarly a countable union of random sets is again a random set, since a hit event is given by the union of individual hit events: The family E of events contains the

Given a random set coming from the imprecise observation of a random variable, we study how to model the information about the distribution of this random variable. Specifically, we investigate whether the information given by the upper and lower probabilities induced by the random set is equivalent to the one given by the class of the distributions of the measurable selections; together with sufficient conditions for this, we also give examples showing that they are not equivalent in all cases.

A pipeline is a popular architecture which connects computational components/filers) through connectors (pipes) so that computations are performed in a stream like fashion. The data are transported through the pipes between filers, gradually transforming inputs to outputs. This kind of stream processing has been made popular through UNIX pipes that serially connect independent components for performing a sequence of tasks. We show in this paper how to formalize this architecture in terms of monads, hereby including relational specifications as special cases. The system is given through a directed acyclic graph the nodes of which carry the computational structure by being labelled with morphisms from the monad, and the edges provide the data for these operations. It is shown how fundamental compositional operations like combining pipes and filers, and refining a system by replacing simple parts through more elaborate ones, are supported through this construction.

We demonstrate the existence of an optimal, individually rational, and incentive compatible selling mechanism for a multiproduct monopolist facing a market populated by consumers with budget constraints. Our main contribution is to show via examples and our existence result that, in general, when facing consumers with budget constraints the monopolist is able to maximize profits over the set of individually rational and incentive compatible selling mechanisms only if other goods are available and only if the monopolist’s goods are nonessential relative to other goods.

no-arbitrage criterion under transaction costs in the case of finite discrete time ∗