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Seminari di Equazioni Differenziali e Applicazioni: Generalized semiconcavity of the value function in (stochastic) optimal control

Venerdì 7 Febbraio 2014, ore 12:15 - Aula 2AB45 - Ermal Feleqi

ARGOMENTI: Seminari

SEMINARIO DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Venerdì 7 Febbraio 2014 alle ore 12:15 in aula 2AB45, Ermal Feleqi (Università di Padova) terrà un seminario dal titolo "Generalized semiconcavity of the value function in (stochastic) optimal control".

Abstract
I will talk about generalized semiconcavity results concerning the value function of a finite horizon stochastic optimal control problem where the state evolves according to a SDE driven by a general L?vy noise with jumps. I will point out how the related analysis reduces to deterministic analysis via moments or Burkholder-Gundy-Davis type inequalities. As a result of this analysis, I will show that it is possible to express a semiconcavity modulus of the value function in terms of certain smoothness and semiconcavity moduli of data. If time allows I may speak also about semiconcavity results in both time and state variables. This is more technical because one has to know how stochastic differentials rescale under affine time changes, the Brownian case is simple and well-known, but for the Poissonian differential one has to appeal to the so-called Kulik's transformation.

Rif. Int. M. Bardi, P. Mannucci, C. Marchi.

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