An Entropy Regularized BSDE Approach to Bermudan Options and Games

Noufel Frikha (), Libo Li () and Daniel Chee ()
Additional contact information
Noufel Frikha: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Libo Li: School of Mathematics and Statistics - UNSW - University of New South Wales [Sydney]
Daniel Chee: School of Mathematics and Statistics - UNSW - University of New South Wales [Sydney]

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: In this paper, we investigate optimal stopping problems in a continuous-time framework where only a discrete set of stopping dates is admissible, corresponding to the Bermudan option, within the so-called exploratory formulation. We introduce an associated control problem for the value function, represented as a non-cadlag reflected backward stochastic differential equation (RBSDE) with an entropy regulariser that promotes exploration, and we establish existence and uniqueness results for this entropy-regularised RBSDE. We then compare the entropy-regularised RBSDE with the theoretical value of a Bermudan option and propose a reinforcement learning algorithm based on a policy improvement scheme, for which we prove both monotone improvement and convergence. This methodology is further extended to Bermudan game options, where we obtain analogous results. Finally, drawing on the preceding analysis, we present two numerical approximation schemes - a BSDE solver based on a temporal-difference scheme and neural networks and the policy improvement algorithm - to illustrate the feasibility and effectiveness of our approach.

Keywords: Bermudan option; Entropy Regularization; Reflected Backward Stochastic Differential Equation; Reinforcement Learning; Policy improvement (search for similar items in EconPapers)
Date: 2025-09-23
Note: View the original document on HAL open archive server: https://hal.science/hal-05265653v1
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-05265653v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-05265653

Access Statistics for this paper

More papers in Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL
Bibliographic data for series maintained by CCSD ().