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12
The Demonic Product of Probabilistic Relations
, 2001
"... 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 nondeterministic fringe of the probabilistic relations behaves properly: the ..."
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Cited by 3 (1 self)
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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 nondeterministic fringe of the probabilistic relations behaves properly: the fringe of the product equals the demonic product of the fringes.
Stochastic relations of random variables and processes
, 2010
"... This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes ..."
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Cited by 3 (3 self)
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This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes preserve some, not necessarily reflexive or transitive, subrelation of the order relation. The main contributions of the paper are: a functional characterization of stochastic relations, necessary and sufficient conditions for the preservation of stochastic relations, and an algorithm for finding subrelations preserved by probability kernels. The theory is illustrated with applications to hidden Markov processes, population processes, and queueing systems.
2006): Noarbitrage and closure results for trading cones with transaction costs
"... 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 cla ..."
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Cited by 2 (2 self)
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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.
Study of the Probabilistic Information of a Random Set
"... 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 equival ..."
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Cited by 2 (2 self)
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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.
Uncountable Intersections of Random Sets
, 1995
"... 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 ..."
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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
Pipes and Filters: Modelling a Software Architecture Through Relations
, 2002
"... 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 proces ..."
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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.
and
"... 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 fa ..."
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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.
Constructive
, 2006
"... noarbitrage criterion under transaction costs in the case of finite discrete time ∗ ..."
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noarbitrage criterion under transaction costs in the case of finite discrete time ∗
Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information
, 2012
"... © The Author(s) 2012. This article is published with open access at Springerlink.com Abstract We study a class of discounted, infinite horizon stochastic games with public and private signals and strategic complementarities. Using monotone operators defined on the function space of values and strate ..."
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© The Author(s) 2012. This article is published with open access at Springerlink.com Abstract We study a class of discounted, infinite horizon stochastic games with public and private signals and strategic complementarities. Using monotone operators defined on the function space of values and strategies (equipped with a product order), we prove existence of a stationary Markov–Nash equilibrium via constructive methods. In addition, we provide monotone comparative statics results for ordered perturbations of our space of games. We present examples from industrial organization literature and discuss possible extensions of our techniques for studying principalagent models.