Skip to content
DraconiticResearch
Search Sources API
185,139 studies31 sourcesUpdated 30 min ago
PreprintarXiv licencearXiv

Aggregation of value processes for semi-martingale BSDEs with jumps

  • Dylan Possamaï
  • Marco Rodrigues
  • Alexandros Saplaouras
Open at sourcePDFDOICite

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.

Related

  1. Coupling for one-dimensional subcritical and critical CBI processes with jumps
    Shukai Chen, Chunhua Ma
    arXivPreprintCC0Full textProbabilityarXiv
  2. First-Passage Time Problems for Jump-Diffusion Processes with Positive and Negative Jumps
    Mario Lefebvre, Antoine Habib
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref
  3. Martingale Posterior Cox Processes
    Joshua Rooijakkers, Edwin Fong
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  4. Uniform Local Asymptotics for Lévy Processes with Subexponential Jumps
    Hao Wu, Wei Xu
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  5. Stochastic Riccati equations with jumps for indefinite linear-quadratic control: A stochastic value-flow approach
    Kai Ding, Jiaqiang Wen, Jie Xiong +1
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{possamai2026aggregation,
  title = {{Aggregation of value processes for semi-martingale BSDEs with jumps}},
  author = {Dylan Possamaï and Marco Rodrigues and Alexandros Saplaouras},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25126},
  eprint = {2609.25126},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25126},
}
RIS
TY  - UNPB
TI  - Aggregation of value processes for semi-martingale BSDEs with jumps
AU  - Dylan Possamaï
AU  - Marco Rodrigues
AU  - Alexandros Saplaouras
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.25126
UR  - https://arxiv.org/abs/2609.25126
AB  - 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.
ER  -