One of the important issues in behavioral analysis is that the time consistency property is lost due to the distortion in performance probability. The standard approach in performance optimization, the dynamic programming, fails to work in this area. In this paper, we propose to use an...

This paper develops an analytical approach to compute the explicit asymptotic formulas for the probability that a time-inhomogeneous diffusion process does not cross a non-flat, lower/upper boundary. We derive the explicit formulas for the first four terms and provide the error bound. The...