Deep Learning in Finance – Lecture 4
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Learning Stochastic Processes Part II: Ito Diffusion
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 13
Venue: Ramanujan Hall
Abstract: This presentation extends the learning of stochastic processes from parameter calibration to the more general problem of discovering stochastic differential equations directly from observed data. The objective is to learn the unknown drift and diffusion coefficients of Itô diffusions using neural networks trained on multiple sample trajectories. Separate learning strategies are developed for time-dependent, state-dependent, and fully general stochastic models, exploiting either explicit analytical solutions when available or Euler discretizations when closed-form solutions do not exist. The methodology estimates the local statistical moments of the process increment and uses them to train neural networks that provide smooth approximations of the drift and volatility functions, leading to the framework of Stochastically Informed Neural Networks (SINNs), a stochastic counterpart of Physics-Informed Neural Networks (PINNs). The approach is illustrated for generalized Brownian motion with drift, generalized geometric Brownian motion, and autonomous Itô diffusions, where suitable transformations, such as the logarithmic transformation for stock-price models, simplify the learning problem. The resulting framework enables the identification of stochastic models directly from data and provides flexible, data-driven representations of time-varying and state-dependent dynamics with applications in finance, physics, engineering, and other scientific disciplines.