Stochastic Optimal Control Problem under Inside Information
Abstract
This paper is concerned with a stochastic optimal control problem under inside information. The control process depends on an ℱT0-measurable random variable Y, representing the static inside information, and is adapted to the enlarged filtration generated by the underlying Brownian motion and the random variable Y. Accordingly, the traditional stochastic integral fails to be well-defined in this non-adapted setting; we adopt forward integrals to formulate the stochastic integral terms in the system. By means of the Donsker delta function, the original controlled system is transformed into a y-parameterized system. We further establish the existence of solutions to forward \textit{stochastic differential equations} (SDEs), and prove the uniqueness of solutions via flow transformation techniques. Under a Gaussian assumption on Y, we derive both necessary and sufficient optimality conditions for the aforementioned control problem. Subsequently, we formulate the \textit{linear-quadratic} (LQ) optimal control problem under inside information. Through the y-parameterized transformation, the original problem is converted into an LQ control problem with random coefficients. A numerical example for the LQ case is provided at the end to validate our theoretical findings.
Related
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BibTeX
@misc{ye2026stochastic,
title = {{Stochastic Optimal Control Problem under Inside Information}},
author = {Yuxin Ye and Jingtao Shi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02164},
eprint = {2609.02164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02164},
note = {CC0},
}
RIS
TY - UNPB
TI - Stochastic Optimal Control Problem under Inside Information
AU - Yuxin Ye
AU - Jingtao Shi
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02164
UR - https://arxiv.org/abs/2609.02164
AB - This paper is concerned with a stochastic optimal control problem under inside information. The control process depends on an ℱ_T_0-measurable random variable Y, representing the static inside information, and is adapted to the enlarged filtration generated by the underlying Brownian motion and the random variable Y. Accordingly, the traditional stochastic integral fails to be well-defined in this non-adapted setting; we adopt forward integrals to formulate the stochastic integral terms in the system. By means of the Donsker delta function, the original controlled system is transformed into a y-parameterized system. We further establish the existence of solutions to forward \textit{stochastic differential equations} (SDEs), and prove the uniqueness of solutions via flow transformation techniques. Under a Gaussian assumption on Y, we derive both necessary and sufficient optimality conditions for the aforementioned control problem. Subsequently, we formulate the \textit{linear-quadratic} (LQ) optimal control problem under inside information. Through the y-parameterized transformation, the original problem is converted into an LQ control problem with random coefficients. A numerical example for the LQ case is provided at the end to validate our theoretical findings.
ER -