2024/09/20 by Yan Wang, Wang, Yan, Yaqi Zhang +3
Engineering · Mathematics · #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.PR
paper · pdf · doi:10.48550/arxiv.2409.13463
28 pages
arxiv created 2026/08/03 · arxiv updated 2026/08/04
With the terminal value |ξ| admitting some given exponential moments, we propose and prove several existence and uniqueness results for the unbounded solutions of quadratic backward stochastic differential equations whose generators may be represented as a uniformly continuous (not necessarily locally Lipschitz continuous) perturbation of some convex/concave function with quadratic growth. This perturbation satisfies various feasible conditions such as boundedness, sub-linear growth or linear growth. In particular, in some cases, the first component of the unique solution can be expressed as the value function of an optimal control problem. These results improves those posed in Delbaen, Hu and Richou [AIHP, 2011] and Fan, Hu and Tang [2020, CRM] to some extent. The critical case is also tackled, which strengthens the main result of Delbaen, Hu and Richou [DCDS, 2011].