Table of Contents Author Guidelines Submit a Manuscript
International Journal of Stochastic Analysis
Volume 2016, Article ID 1018509, 6 pages
http://dx.doi.org/10.1155/2016/1018509
Research Article

Generalisation of Hajek’s Stochastic Comparison Results to Stochastic Sums

IAM, Heidelberg University, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany

Received 31 March 2016; Revised 23 June 2016; Accepted 17 July 2016

Academic Editor: Lukasz Stettner

Copyright © 2016 Jörg Kampen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Hajek’s univariate stochastic comparison result is generalised to multivariate stochastic sum processes with univariate convex data functions and for univariate monotonic nondecreasing convex data functions for processes with and without drift, respectively. As a consequence strategies for a class of multivariate optimal control problems can be determined by maximizing variance. An example is passport options written on multivariate traded accounts. The argument describes a narrow path between impossibilities of generalisations to jump processes or impossibilities of more general data functions.