A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Xiong, Jie, Yang, Ying
Institution: Southern University of Science and Technology
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Awards: G1351101462, G259192822
OpenAlex ID: W7164195242