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arXiv · 2609.25126

Aggregation of value processes for semi-martingale BSDEs with jumps

Dylan Possamaï·Marco Rodrigues·Alexandros Saplaouras
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Abstract

We construct a measurable aggregator for the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs) with jumps. The results can be applied to control problems where the triplet of semi-martingale characteristics is controlled in a possibly non-dominated case or where uncertainty about the characteristics is present in the optimisation. The construction also provides a time-consistent system of fully nonlinear conditional expectations on the Skorokhod space. We also construct an appropriate path-regularisation of the value function and prove a corresponding dynamic programming principle. The generality we seek allows for the treatment of controlled diffusions, pure-jump processes, and discrete-time processes in a unified setting.

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Dylan Possamaï, Marco Rodrigues, Alexandros Saplaouras. 2026-09-20. Aggregation of value processes for semi-martingale BSDEs with jumps. https://arxiv.org/abs/2609.25126

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