Robust Control for Marked Point Processes under Transition-Rate Uncertainty

Sascha Desmettre; Philipp C. Hornung

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arXiv · 2607.16935

Robust Control for Marked Point Processes under Transition-Rate Uncertainty

Sascha Desmettre·Philipp C. Hornung

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Abstract

We consider a novel robust utility maximisation problem under bounded cumulative transition rate uncertainty within the class of non-Markovian marked point processes on a finite state-space. Utility is maximised over the class of admissible controls, while Nature chooses a worst-case biometric scenario from the class of admissible, path-dependent cumulative transition rates restricted by path-dependent upper and lower bounds. We prove a martingale optimality principle and a novel existence and uniqueness result for a non-standard worst-case backwards stochastic differential equation, which allows us to establish existence and uniqueness of worst-case and best-case prospective reserves of life and health insurance contracts with reserve-dependent payments. Finally, we find an explicit solution of a novel robust consumption-insurance problem with power utility preferences.

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BibTeX RIS

Sascha Desmettre, Philipp C. Hornung. 2026-07-18. Robust Control for Marked Point Processes under Transition-Rate Uncertainty. https://arxiv.org/abs/2607.16935

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