BSDE with Jumps When Mean Reflection Is Nonlinear - Winfrida Felix Mwigilwa; Farai Julius Mhlanga (International Journal of Mathematics and Mathematical Sciences)
In this paper, we investigate a reflected backward stochastic differential equation (RBSDE) with jumps, focusing on cases where the mean reflection is nonlinear. Unlike traditional RBSDEs, this particular type of RBSDE imposes a constraint defined by the mean of a loss function that does not follow the continuous condition. We start by deriving an a priori estimate of the solution, followed by establishing the uniqueness and existence of the solution. Theoretical results are illustrated by way of an example of the application of super-hedging to the reinsurance and investment problem under a risk constraint.