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Pré-Publication, Document De Travail Année : 2023

Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control

Xiaomin Shi
  • Fonction : Auteur
Zuo Quan Xu
  • Fonction : Auteur

Résumé

In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for one-dimensional case. Using these and other delicate tools, we then construct solutions to coupled two-dimensional stochastic Riccati equation with jumps in both standard and singular cases. In the end, these results are applied to solve a cone-constrained stochastic linear-quadratic and a mean-variance portfolio selection problem with jumps. Different from no jump problems, the optimal (relative) state processes may change their signs, which is of course due to the presence of jumps.
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Dates et versions

hal-04364600 , version 1 (27-12-2023)

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Ying Hu, Xiaomin Shi, Zuo Quan Xu. Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control. 2023. ⟨hal-04364600⟩
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