Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility
Ziteng Cheng, Ph.D. Student, Department of Applied Mathematics, Illinois Institute of Technology
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 is the very first step towards realizing the objective of deriving Wiener-Hopf type factorizations for (real-valued) time-inhomogeneous Levy processes. In particular, we argue that the classical Wiener-Hopf factorization for time-homogeneous Levy processes quite likely does not carry over to the case of time-inhomogeneous Levy processes. This is joint work with Tomasz R. Bielecki and Ruoting Gong.
Mathematical Finance, Stochastic Analysis, and Machine Learning