A Minimal Set of Shannon-type Inequalities for Functional Dependence Structures

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given inequality is a constrained Shannon-type inequality. Another important application of elemental inequalities is to formulate and compute the Shannon outer bound for multi-source multi-sink network coding capacity. Under this formulation, it is the region of feasible source rates subject to the elemental inequalities and network coding constraints that is of interest. Hence it is of fundamental interest to identify the redundancies induced amongst elemental inequalities when given a set of functional dependence constraints. In this paper, we characterize a minimal set of Shannon-type inequalities when functional dependence constraints are present.Comment: 5 pagers, accepted ISIT201

"Convertible Bond Underpricing: Renegotiable Covenants, Seasoning and Convergence"

We investigate the long-standing puzzle on the underpricings of convertible bonds. We hypothesize that the observed underpricing is induced by the possibility that a convertible bond might renegotiate on some of its covenants, e.g., an imbedded put option, in financial difficulties. Consistent with our hypothesis, we find that the initial underpricing is larger for lower rated bonds. The underpricing worsens if the issuer experiences subsequent financial difficulties. However, conditional on no rating downgrades, our main empirical result shows that convertible bond prices do converge to their theoretical prices within two years. This seasoning period is shorter for higher rated convertible bonds.