A class of stochastic control problems with state constraints

Tiziano De Angelis and Erik Ekstr\"om

Papers from arXiv.org

Abstract: We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in order to keep the time-space process $(t,X_t)$ inside the set $\mathcal{C}:=([0,T]\times\mathbb{R}^d)\setminus\mathcal{D}$, while at the same time minimising an expected cost that depends on the state $(t,X_t)$ and is quadratic in the speed of the control exerted. We find a probabilistic representation for the value function and an optimal control under a set of mild sufficient conditions concerning the coefficients of the underlying dynamics and the regularity of the set $\mathcal{D}$. The optimally controlled dynamics is in strong form, in the sense that it is adapted to the filtration generated by the driving Brownian motion. Fully explicit formulae are presented in some relevant examples.

Date: 2026-03
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2603.04880 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:2603.04880

Access Statistics for this paper

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