Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility

Tomasz R. Bielecki, Ziteng Cheng, Ruoting Gong

Published 2020-06-02Version 1

In this paper we obtain a Wiener-Hopf type factorization for a time-inhomogeneous arithmetic Brownian motion with deterministic time-dependent drift and volatility. To the best of our knowledge, this paper is the very first step towards realizing the objective of deriving Wiener-Hopf type factorizations for (real-valued) time-inhomogeneous L\'{e}vy processes. In particular, we argue that the classical Wiener-Hopf factorization for time-homogeneous L\'{e}vy processes quite likely does not carry over to the case of time-inhomogeneous L\'{e}vy processes.