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2020 Probabilistic interpretation of HJB equations by the representation theorem for generators of BSDEs
Lishun Xiao, Shengjun Fan, Dejian Tian
Electron. Commun. Probab. 25(none): 1-10 (2020). DOI: 10.1214/20-ECP310

Abstract

The purpose of this note is to propose a new approach for the probabilistic interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic recursive optimal control problems, utilizing the representation theorem for generators of backward stochastic differential equations. The key idea of our approach for proving this interpretation lies in the identity between solutions and generators given by the representation theorem. Compared with existing methods, our approach seems to be a feasible unified method for different frameworks and be more applicable to general settings. This can also be regarded as a new application of such representation theorem.

Citation

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Lishun Xiao. Shengjun Fan. Dejian Tian. "Probabilistic interpretation of HJB equations by the representation theorem for generators of BSDEs." Electron. Commun. Probab. 25 1 - 10, 2020. https://doi.org/10.1214/20-ECP310

Information

Received: 24 April 2019; Accepted: 18 March 2020; Published: 2020
First available in Project Euclid: 9 April 2020

zbMATH: 07204052
MathSciNet: MR4089737
Digital Object Identifier: 10.1214/20-ECP310

Subjects:
Primary: 35K20, 49L25, 60H10

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