Online Drift Estimation for Jump-Diffusion Processes

46 Pages Posted: 10 Mar 2020 Last revised: 5 Feb 2021

See all articles by Theerawat Bhudisaksang

Theerawat Bhudisaksang

University of Oxford - Mathematical Institute

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: February 18, 2020

Abstract

We show the convergence of an online stochastic gradient descent estimator to obtain the drift parameter of a continuous-time jump-diffusion process. The stochastic gradient descent follows a stochastic path in the gradient direction of a function to find a minimum, which in our case determines the estimate of the unknown drift parameter. We decompose the deviation of the stochastic descent direction from the deterministic descent direction into four terms: the weak solution of the non-local Poisson equation, a Riemann integral, a stochastic integral, and a covariation term. This decomposition is employed to prove the convergence of the online estimator and we use simulations to illustrate the performance of the online estimator.

Keywords: SGDCT, online estimation, jump-diffusion, extended Ito lemma, non-local Poisson equation, Levy process

JEL Classification: C1, C13, C15, C22

Suggested Citation

Bhudisaksang, Theerawat and Cartea, Álvaro, Online Drift Estimation for Jump-Diffusion Processes (February 18, 2020). Available at SSRN: https://ssrn.com/abstract=3540252 or http://dx.doi.org/10.2139/ssrn.3540252

Theerawat Bhudisaksang (Contact Author)

University of Oxford - Mathematical Institute ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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