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Generalized semiconcavity of the value function of a jump diffusion optimal control problem

Feleqi, Ermal 2015. Generalized semiconcavity of the value function of a jump diffusion optimal control problem. Nonlinear Differential Equations and Applications NoDEA 22 (4) , pp. 777-809. 10.1007/s00030-014-0304-z

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Abstract

Generalized semiconcavity results for the value function of a jump diffusion optimal control problem are established, in the state variable, uniformly in time. Moreover, the semiconcavity modulus of the value function is expressed rather explicitly in terms of the semiconcavity or regularity moduli of the data (Lagrangian, terminal cost, and terms comprising the controlled SDE), at least under appropriate restrictions either on the class of the moduli, or on the SDEs. In particular, if the moduli of the data are of power type, then the semiconcavity modulus of the value function is also of power type. An immediate corollary are analogous regularity properties for (viscosity) solutions of certain integro-differential Hamilton-Jacobi-Bellman equations, which may be represented as value functions of appropriate optimal control problems for jump diffusion processes.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 1021-9722
Date of First Compliant Deposit: 1 December 2016
Date of Acceptance: 9 December 2014
Last Modified: 13 Mar 2019 12:37
URI: http://orca.cf.ac.uk/id/eprint/96520

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