A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations
Abstract
This paper studies a partially observed stochastic optimal control problem for jump-diffusion states observed through multivariate counting processes with state-dependent intensities. Because the observation jumps carry information about the latent state through their intensities, the variational analysis involves coupled state and likelihood-ratio perturbations. By introducing a reference probability measure and augmenting the state with the counting-process likelihood ratio, we establish a stochastic maximum principle whose first-order necessary condition is expressed as a conditional Hamiltonian stationarity relation with respect to the observation filtration. Finally, an LQ example is used to examine the compatibility of a linear adjoint ansatz and to illustrate numerically the coupled partial-information stationarity system.
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BibTeX
@misc{xiong2026stochastic,
title = {{A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations}},
author = {Jie Xiong and Ying Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10844},
eprint = {2606.10844},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.10844},
}
RIS
TY - UNPB
TI - A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations
AU - Jie Xiong
AU - Ying Yang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2606.10844
UR - https://arxiv.org/abs/2606.10844
AB - This paper studies a partially observed stochastic optimal control problem for jump-diffusion states observed through multivariate counting processes with state-dependent intensities. Because the observation jumps carry information about the latent state through their intensities, the variational analysis involves coupled state and likelihood-ratio perturbations. By introducing a reference probability measure and augmenting the state with the counting-process likelihood ratio, we establish a stochastic maximum principle whose first-order necessary condition is expressed as a conditional Hamiltonian stationarity relation with respect to the observation filtration. Finally, an LQ example is used to examine the compatibility of a linear adjoint ansatz and to illustrate numerically the coupled partial-information stationarity system.
ER -