$\epsilon$-Monotone Fourier Methods for Optimal Stochastic Control in Finance

Peter A. Forsyth and George Labahn

Papers from arXiv.org

Abstract: Stochastic control problems in finance often involve complex controls at discrete times. As a result numerically solving such problems, for example using methods based on partial differential or integro-differential equations, inevitably give rise to low order accuracy, usually at most second order. In many cases one can make use of Fourier methods to efficiently advance solutions between control monitoring dates and then apply numerical optimization methods across decision times. However Fourier methods are not monotone and as a result give rise to possible violations of arbitrage inequalities. This is problematic in the context of control problems, where the control is determined by comparing value functions. In this paper we give a preprocessing step for Fourier methods which involves projecting the Green's function onto the set of linear basis functions. The resulting algorithm is guaranteed to be monotone (to within a tolerance), $\ell_\infty$-stable and satisfies an $\epsilon$-discrete comparison principle. In addition the algorithm has the same complexity per step as a standard Fourier method while at the same time having second order accuracy for smooth problems.

Date: 2017-10, Revised 2018-04
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/1710.08450 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1710.08450

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().