Characteristic-sorted portfolios are the workhorses of modern empirical finance, deployed widely to evaluate anomalies and construct asset pricing models. We propose a new method for their estimation that is simple compute, makes no ex-ante assumption on nature relationship between characteristic returns, does not require ad hoc selections percentile breakpoints or portfolio weighting schemes. ...

Let P ∈ Q <m...

These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. I sometimes edit the notes after class to make them way what I wish I had said. There may be small mistakes, so I recommend that you check any mathematically precise statement before using it in your own work. These notes were last revised on Decemb...

Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...

This paper shows how modal mu-calculus formulae characterizing finite-state processes up to strong or weak bisimulation can be derived directly from the well-known greatest fixpoint characterizations of the bisimulation relations. Our derivation simplifies earlier proofs for the strong bisimulation case and, by virtue of derivation, immediately generalizes to various other bisimulation-like rel...

We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.