The first-crossing-time problem through two time-dependent boundaries for one-dimensional diffusion processes is considered. The first crossing p.d.f.'s from below and from above are proved to satisfy a new system of Volterra integral equations of the second kind involving two arbitrary continuous functions. By a suitable choice of such functions a system of continuous--kernel integral equations is obtained and an efficient algorithm for its solution is provided. Finally, conditions on the drift and infinitesimal variance of the diffusion process are given such that the system of integral equations reduce to a non-singular single integral equation for the first-crossing-time p.d.f.
On the two boundary first–crossing–time problem for diffusion processes
GIORNO, Virginia;NOBILE, Amelia Giuseppina;
1990-01-01
Abstract
The first-crossing-time problem through two time-dependent boundaries for one-dimensional diffusion processes is considered. The first crossing p.d.f.'s from below and from above are proved to satisfy a new system of Volterra integral equations of the second kind involving two arbitrary continuous functions. By a suitable choice of such functions a system of continuous--kernel integral equations is obtained and an efficient algorithm for its solution is provided. Finally, conditions on the drift and infinitesimal variance of the diffusion process are given such that the system of integral equations reduce to a non-singular single integral equation for the first-crossing-time p.d.f.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
