The Trotter-Kato Approximation in Utility Maximization

  • Author / Creator
    Miao, Lingyu
  • This thesis deals with the Trotter-Kato approximation in utility maximization. The Trotter-Kato approximation is a method to split a differential equation into two parts, which are then solved iteratively over small time intervals. In the context of utility maximization, this procedure was introduced by Nadtochiy and Zariphopoulou [11] for partial differential equations (PDEs) in a Markovian setting, which we revisit in the first part of this thesis. We then study what the Trotter-Kato approximation can mean for backward stochastic differential equations (BSDEs), which do not need Markovian assumptions and allow for a probabilistic interpretation. We also discuss how the Trotter- Kato approximation can be implemented numerically in both the PDE and the BSDE case.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • 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.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematical Finance
  • Supervisor / co-supervisor and their department(s)
    • Frei, Christoph (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Frei, Christoph (Department of Mathematical and Statistical Sciences)
    • Melnikov, Alexander (Department of Mathematical and Statistical Sciences)
    • Cadenillas, Abel (Department of Mathematical and Statistical Sciences)
    • Schmuland, Byron (Department of Mathematical and Statistical Sciences)