Approximate expected hitting times of certain state variables of physics and economics

Abstract

In this paper we study expectations of hitting times of certain physically and economically relevant state variables in the presence of two fixed boundary planes. An asymptotic expansion is developed for the mean of the hitting-time distribution for a process X(t) whose rate of change V(t) is driven by a Brownian motion process and over which a linear deterministic term is superimposed. A truncated version of this expansion is proposed as an approximation to the true mean first passage time. In a series of simulations, the approximation is found to perform well even in nonasymptotic regions.