Using high-frequency data, we decompose the time-varying beta for stocks into beta for continuous systematic risk and beta for discontinuous systematic risk. Estimated discontinuous betas for S&P500 constituents between 2003 and 2011 generally exceed the corresponding continuous betas. We demonstrate how continuous and discontinuous betas decrease with portfolio diversification. Using an equiwe...

Over the last few years, several mixed discontinuous Galerkin finite element methods (DGFEM) have been proposed for the discretization of incompressible fluid flow problems. We mention here only the piecewise solenoidal discontinuous Galerkin methods introduced in [5,25], the local discontinuous Galerkin methods of [12,11], and the interior penalty methods studied in [24,33,18]. Some of the mai...

Abstract We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of singular subanalytic germs. The main novelty our approach is allow “moderately discontinuous” chains, are specially advantageous for capturing the subtleties outer phenomena. Our invariant finitely generated graded abelian group any and homomorphisms ....