67 research outputs found
Ultramodular functions.
We study the properties of ultramodular functions, a class of functions that generalizes scalar convexity and that naturally arises in some economic and statistical applications.
Characterizations of bivariate conic, extreme value, and Archimax copulas
Based on a general construction method by means of bivariate ultramodular copulas we construct, for particular settings, special bivariate conic, extreme value, and Archimax copulas. We also show that the sets of copulas obtained in this way are dense in the sets of all conic, extreme value, and Archimax copulas, respectively
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Copulae: On the Crossroads of Mathematics and Economics
The central focus of the workshop was on copula theory as well as applications to multivariate stochastic modelling. The programme was intrinsically interdisciplinary and represented areas with much recent progress. The workshop included talks and dynamic discussions on construction, estimation and various applications of copulas to finance, insurance, hydrology, medicine, risk management and related fields
Monotonic Mechanisms for Selling Multiple Goods
Maximizing the revenue from selling two or more goods has been shown to
require the use of mechanisms, where a higher-valuation buyer
may pay less than a lower-valuation one. Here we show that the restriction to
mechanisms may not just lower the revenue, but may in fact yield
only a of the maximal revenue; more precisely, the
revenue from monotonic mechanisms is no more than k times the simple revenue
obtainable by selling the goods separately, or bundled (where k is the number
of goods), whereas the maximal revenue may be arbitrarily larger. We then study
the class of monotonic mechanisms and its subclass of allocation-monotonic
mechanisms, and obtain useful characterizations and revenue bounds.Comment: http://www.ma.huji.ac.il/hart/publ.html#mech-mono
On Concavity and Supermodularity
Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [2] and Konig [5].Concavity, Supermodularity
On convexity and supermodularity.
Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [1] and Konig [4].
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