Joint time-state generalized semiconcavity of the value function of a jump diffusion optimal control problem

Feleqi, Ermal ORCID: https://orcid.org/0000-0002-9661-0684 2019. Joint time-state generalized semiconcavity of the value function of a jump diffusion optimal control problem. Nonlinear Differential Equations and Applications 26 (1) , 4. 10.1007/s00030-018-0550-6

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Abstract

We prove generalized semiconcavity results, jointly in time and state variables, for the value function of a stochastic finite horizon optimal control problem, where the evolution of the state variable is described by a general stochastic differential equation (SDE) of jump type. Assuming that terms comprising the SDE are C1-smooth, and that running and terminal costs are semiconcave in generalized sense, we show that the value function is also semiconcave in generalized sense, estimating the semiconcavity modulus of the value function in terms of smoothness and generalized semiconcavity moduli of data. Of course, these translate into analogous regularity results for (viscosity) solutions of integro-differential Hamilton–Jacobi–Bellman equations due to their controllistic interpretation. This paper may be seen as a sequel to Feleqi (Dyn Games Appl 3(4):523–536, 2013), where we dealt with the generalized semiconcavity of the value function only in the state variable.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/)
Publisher:	Springer Verlag (Germany)
ISSN:	1021-9722
Date of First Compliant Deposit:	10 May 2021
Date of Acceptance:	26 December 2018
Last Modified:	02 May 2023 17:37
URI:	https://orca.cardiff.ac.uk/id/eprint/141133

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