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BSDE with Jumps When Mean Reflection Is Nonlinear

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  • Winfrida Felix Mwigilwa
  • Farai Julius Mhlanga
  • Bilal Bilalov

Abstract

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.

Suggested Citation

  • Winfrida Felix Mwigilwa & Farai Julius Mhlanga & Bilal Bilalov, 2024. "BSDE with Jumps When Mean Reflection Is Nonlinear," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2024, pages 1-16, July.
    • Handle: RePEc:hin:jijmms:9963889
    DOI: 10.1155/2024/9963889
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