On the inverse first-passage-time problem for a wiener process

Abstract

The inverse first-passage problem for a Wiener process (Wt) t≤0 seeks to determine a function b : ℝ+→ℝ such that τ = inf{t > 0|Wt ge; b(t)} has a given law. In this paper two methods for approximating the unknown function b are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.