Let Xt be a subordinate Brownian motion, and suppose that the Lévy measure of the underlying subordinator has a completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(τxt) of first passage times τx through a barrier at x0, and its...

Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider...