Communications in Mathematical Sciences

Volume 18 (2020)

Number 1

Optimal stopping via reinforced regression

Pages: 109 – 121



Denis Belomestny (Faculty of Maths., Duisburg-Essen Univ., Essen, Germany; Faculty of Computer Sci., National Univ. Higher School of Economics, Moscow, Russia; and Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia)

John Schoenmakers (Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany)

Vladimir Spokoiny (WIAS, Berlin, Germany; Departments of Mathematics and Economics, Humboldt-Universität zu Berlin, Germany; Faculty of Computer Science, HSE, Moscow, Russia; and IITP RAS, Moscow, Russia)

Bakhyt Zharkynbay (Faculty of Computer Science, HSE, Moscow, Russia)


In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression-based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each backward induction step by adding new basis functions based on the previously estimated continuation values. The proposed methodology is illustrated by several numerical examples from mathematical finance.


Monte Carlo, optimal stopping, regression, reinforcement

2010 Mathematics Subject Classification

60H35, 62P05, 65C05

This work was supported by the Russian Science Foundation (RSF) grant 19-71-30020 and by the Excellence Cluster Math+ Berlin, project AA4-2.

Accepted 3 September 2019

Published 1 April 2020