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arXiv · 2603.25486

Stochastic maximum principle for time-changed forward-backward stochastic control problem with L\'evy noise

Jingwei Chen·Jun Ye·Feng Chen
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Abstract

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational time (the inverse of an $\alpha$-stable subordinator) to model phenomena like trapping events and subdiffusion. Using a duality transformation and the convex variational method, we derive necessary and sufficient conditions for optimality, expressed through a novel set of adjoint equations. Finally, the theoretical results are applied to solve an explicit cash management problem under stochastic recursive utility.

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Jingwei Chen, Jun Ye, Feng Chen. 2026-03-26. Stochastic maximum principle for time-changed forward-backward stochastic control problem with L\'evy noise. https://arxiv.org/abs/2603.25486

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