First passage time densities of Brownian motion and applications to credit risk.

摘要

In this thesis we address two related problems: First, we introduce a new approach and derive, a closed form representation of the density of the stopping time tf:=inft≥0&vbm0; Bt=ft in the case in which B is one-dimensional Brownian motion and the barrier f is strictly positive, nondecreasing and right-continuous (without the usual restrictions of differentiability, concavity, and convexity). Second, we introduce a new methodology to study the probability of default in the case in which both the assets V and liabilities L are stochastic and possibly correlated.