Reflected Backward Stochastic Differential Equations for Informational Systems with Applications

• Author / Creator

  Alsheyab, Safa' Mahmoud

• The core innovation of this thesis lies in studying reflected backward stochastic differential equations (RBSDE hereafter) for informational systems. An informational system is a system where there is discrepancy in the information received by agents over time. In this thesis, we restrict to the case where our system is governed by two flows of informations: The public information F that is available to all agents and a larger flow of information G that has additional information about a random time T. We mathematically formulate our results in a general setting where T might not be observable by the flow of information F. This allows our results to be applicable to credit risk theory, to life insurance where mortality and longevity risks are the main challenges, to financial models with arbitrary random horizon, ..., etcetera. Thus, we study RBSDEs that are stopped at T, and consider G to be the progressive enlargement of F with T, where T becomes an observable time when it occurs (a stopping time with respect to G mathematically speaking). In this setting, we quantify --as explicit as possible-- the impact of T on the existence, the uniqueness, and the estimate in norm of the solution of the RBSDE stopped at T. We construct an RBSDE under F that is intimately related to the stopped one, and we single out the exact relationship between their solutions. Importantly, we prove that for any random time, having a positive Az\'ema supermartingale, there exists a positive discount factor E, which is a positive and non-increasing F-adapted and RCLL process, that is vital in proving our results without assuming any further assumption on T. We treat both the linear and general cases of RBSDEs for bounded and unbounded horizon.

• Subjects / Keywords

  • Reflected Backward Stochastic Differential Equations
  • BSDEs
  • Informational systems
  • Random horizon
  • Prior Estimates
  • Exponential Hedging

• Graduation date

  Spring 2022

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-4y6k-ky55

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.