Continuity of Utility Maximization under Weak Convergence

28 Pages Posted: 7 Nov 2018 Last revised: 6 Dec 2018

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yan Dolinsky

ETH Zürich

Jia Guo

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: November 4, 2018

Abstract

In this paper we find sufficient conditions for the continuity of the value of the utility maximization
problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We provide several examples which illustrate that without these conditions, we cannot generally expect continuity to hold. Finally, we apply our results to the computation of the minimum shortfall in the Heston model by building an appropriate lattice approximation.

Keywords: Incomplete Markets, Utility Maximization, Weak Convergence

Suggested Citation

Bayraktar, Erhan and Dolinsky, Yan and Guo, Jia, Continuity of Utility Maximization under Weak Convergence (November 4, 2018). Available at SSRN: https://ssrn.com/abstract=3278294 or http://dx.doi.org/10.2139/ssrn.3278294

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yan Dolinsky

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Jia Guo

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

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