Stochastic optimal control with measurable coefficients via $L^p$-viscosity solutions and applications to optimal advertising

Filippo de Feo

Papers from arXiv.org

Abstract: Stochastic optimal control control problems with merely measurable coefficients are not well understood. In this manuscript, we consider fully non-linear stochastic optimal control problems in infinite horizon with measurable coefficients and (local) uniformly elliptic diffusion. Using the theory of $L^p$-viscosity solutions, we show existence of an $L^p$-viscosity solution $v\in W_{\rm loc}^{2,p}$ of the Hamilton-Jacobi-Bellman (HJB) equation, which, in turn, is also a strong solution (i.e. it satisfies the HJB equation pointwise a.e.). We are then led to prove verification theorems, providing necessary and sufficient conditions for optimality. These results allow us to construct optimal feedback controls and to characterize the value function as the unique $L^p$-viscosity solution of the HJB equation. To the best of our knowledge, these are the first results for fully non-linear stochastic optimal control problems with measurable coefficients. We use the theory developed to solve a stochastic optimal control problem arising in economics within the context of optimal advertising.

Date: 2025-02, Revised 2026-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2502.02352 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2502.02352

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().