A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations

Jie Xiong; Ying Yang

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arXiv · 2606.10844

A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations

Jie Xiong·Ying Yang

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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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Jie Xiong, Ying Yang. 2026-09-22. A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations. https://arxiv.org/abs/2606.10844

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