Explicit solution of an inverse first-passage time problem for lévy processes and counterparty credit risk

Abstract

For a given Markov process X and survival function H on ℝ+, the inverse first-passage time problem (IFPT) is to find a barrier function b :ℝ+→ [-∞,+∞] such that the survival function of the first-passage time τb = inf{t ≥ 0 :X(t)