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Dedicated to Professor Robert Lowen on the occasion of his sixtieth birthday MSC: 54E15 54B20 54D35 54E55 Keywords: Stable filter Cauchy filter Hausdorff quasi-uniformity Bicompletion Uniform space Quasi-uniform space Doubly stable Double cluster pointWe study conditions under which the Hausdorff quasi-uniformity U H of a quasi-uniform space (X, U) on the set P 0 (X) of the nonempty subsets of X is bicomplete.Indeed we present an explicit method to construct the bicompletion of the T 0 -quotient of the Hausdorff quasi-uniformity of a quasi-uniform space. It is used to find a characterization of those quasi-uniform T 0 -spaces (X, U) for which the Hausdorff quasi-uniformity U H of their bicompletion ( X, U ) on P 0 ( X) is bicomplete.

Abstract. The concept of semicompleteness (weaker than half-completeness) is de ned for the Bourbaki quasi-uniformity of the hyperspace of a quasi-uniform space. It is proved that the Bourbaki quasi-uniformity is semicomplete in the space of nonempty sets of a quasi-uniform space (X; U) if and only if each stable lter on (X; U ) has a cluster point in (X; U). As a consequence the space of nonempty sets of a quasi-pseudometric space is semicomplete if and only if the space itself is half-complete. It is also given a characterization of semicompleteness of the space of nonempty U -compact sets of a quasi-uniform space (X; U) which extends the well known Zenor-Morita theorem.2000 AMS Classi cation: 54E15, 54E35, 54B20.

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Executive summary:This paper evaluates the performance of several skewed and symmetric distributions in modeling the tail behavior of daily returns and forecasting Value at Risk (VaR). First, we used