{"ID":2899233,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.01767","arxiv_id":"2507.01767","title":"Mind the jumps: when 2BSDEs meet semi-martingales","abstract":"We construct an aggregated version of 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). 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 find the semi-martingale decomposition of the value function and characterise it as the solution to a semi-martingale second-order BSDE. The generality we seek allows for the treatment of controlled diffusions, pure-jump processes, and discrete-time processes in a unified setting.","short_abstract":"We construct an aggregated version of 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). The results can be applied to control problems where the triplet of semi-martingale characte...","url_abs":"https://arxiv.org/abs/2507.01767","url_pdf":"https://arxiv.org/pdf/2507.01767v1","authors":"[\"Dylan Possamaï\",\"Marco Rodrigues\",\"Alexandros Saplaouras\"]","published":"2025-07-02T14:47:07Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}