Stochastic areas of diffusions and applications

In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time-change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform and integer moments of the stochastic area in terms of the eigenfunctions of the associated diffusion. We show applications of the results to a new structural model of default (Yildirim [28]) and the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang [11]).