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

  • Ermal FeleqiEmail author


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.

Mathematics Subject Classification

35D10 35E10 60H30 93E20 


Generalized semiconcavity Value function Optimal control Partial integro-differential equations Hammilton-Jacobi-Bellman equations Jump diffusions 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PadovaPadovaItaly

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