Convertible bonds give rise to the so-called free boundary; i.e., an unknownboundary between continuation and conversion regions of the bond. Thecharacteristic feature of such a bond, with an extra call feature, is that thefree boundary may reach all the way to the fixed boundary. Our intention inthis paper is to study the behavior of the free boundary in the vicinity of atouching point with the fixed boundary. Along the lines of our analysis we willalso produce some results on regularity of solutions (value of the bond) up tothe fixed boundary. Our methods are robust and of general nature, and can beapplied to fully nonlinear equations. In particular, we shall obtain uniformresults for the regularity of both solutions and their free boundaries.
展开▼
