Robust estimation of multivariate jump-diffusion processes via Dynamic Programming

In this work we present a framework for estimation of a rather general class of multivariate jump-diffusion processes. We assume that a continuous unobservable linear diffusion processes system is additively mixed together with a discrete jump processes vector and a conventional multi-variate white-noise process. This sum is observed over time as a multi-variate jump-diffusion time-series. Our objective is to identify realizations of all components of the mix in a robust and scalable way. First, we formulate this model as an Mixed-Integer-Programming (MIP) optimization problem extending traditional least-squares estimation framework to include discrete jump processes. Then we propose a Dynamic Programming (DP) approximate algorithm that is reasonably fast & accurate and scales polynomially with time horizon. Finally, we provide numerical test cases illustrating the algorithm performance and robustness.