Time-symmetric optimal stochastic control problems in space-time domains. (2nd November 2022)

• Record Type: Journal Article
• Authors: Cruzeiro, Ana Bela; Oliveira, Carlos; Zambrini, Jean-Claude
• Is Part Of: Optimization. Volume 71:Number 11(2022)
• Page Start: 3241
• Page End: 3275
• Publication Date: 2022-11-02
• Subjects: Bernstein processes on random time intervals -- stochastic optimal control -- hidden diffusions -- free boundary PDEs; 60H30 -- 60H10 -- 35R35 -- 93E20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2017430
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of 'Schrödinger's problem' (1931–1932) to space-time domains. The relation with the notion of 'Hidden diffusions' is also described.