The Trotter-Kato Approximation in Utility Maximization
Date
Author
Institution
Degree Level
Degree
Department
Specialization
Supervisor / Co-Supervisor and Their Department(s)
Examining Committee Member(s) and Their Department(s)
Citation for Previous Publication
Link to Related Item
Abstract
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.