On the infinite-dimensional representation of stochastic controlled systems with delayed control in the diffusion term

Giorgio Fabbri and Salvatore Federico ()

No 14-06, Documents de recherche from Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne

Abstract: In the deterministic context a series of well established results allow to reformu- late delay differential equations (DDEs) as evolution equations in infinite dimensional spaces. Several models in the theoretical economic literature have been studied using this reformulation. On the other hand, in the stochastic case only few results of this kind are available and only for specific problems. The contribution of the present letter is to present a way to reformulate in infinite dimension a prototype controlled stochastic DDE, where the control variable appears delayed in the diffusion term. As application, we present a model for quadratic risk minimization hedging of European options with execution delay and a time-to-build model with shock. Some comments concerning the possible employment of the dynamic programming after the reformulation in infinite dimension conclude the letter.

Keywords: Stochastic delay differential equations; Evolution equations in Hilbert space; Dynamic programming (search for similar items in EconPapers)
JEL-codes: C61 G11 O40 (search for similar items in EconPapers)
Pages: 12 pages
Date: 2014
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Related works:
Journal Article: On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term (2014)
Working Paper: On the infinite-dimensional representation of stochastic controlled systems with delayed control in the diffusion term (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eve:wpaper:14-06

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