Stochastic optimal control different in finance and engineering
My introductory answer is that engineering they does use those methods if the situation calls for it. First, the development and implementation of computers suitable for financial use (e.g. high frequency trading) is both a finance and engineering problem: financial engineering is a discipline.

In control systems we try to establish a general model that describes how the system works and that dictates what types of inputs our controller should be prepared to anticipate. Stock markets are better modeled by geometric Brownian motion, for which the Black-Scholes equation offers a solution. Many control problems in control systems engineering will involve some study of standard Brownian motion and Wiener processes. Brownian motion has a basis in physics.

The DSP Stack Exchange would probably give more insight answers, since that finance data and physical data are both just signals from the perspective of that field, and signal processing methods apply to them.