Numerical Analysis Seminars: Duality-based error estimates for some approximation schemes for optimal investment problems
29 January 2016 14:00 in CM105
Duality methods represent a powerful tool for solving optimal investment/consumption problems. We focus on a model similar to Cuoco and Liu (2000) who establish a duality relation in continuous time. A synthesis of the usual arguments, most of them based on the seminal work of Kramkov and Schachermayer (1999), can be found in a note of Rogers (2001). Referring to their abstract framework, we investigate the duality relation between a class of semi-discrete approximations of the primal and dual problem. It will then be shown how the results can be applied in order to derive error bounds for the numerical schemes under consideration. In particular, the dual result allows us to by-pass a generally applicable, but in this case pessimistic bound proved by Krylov (1999) for the control approximation.
Contact David.Bourne@durham.ac.uk for more information