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

Abstract

The inverse first-passage problem for a Wiener process (W_t)_t≥0 seeks to determine a function b: ℝ₊→ℝ such that

τ=inf{t>0|W_t≥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.