Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T10:36:01.943Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Time to Exchange Two Baskets

Part of: Stochastic processes Sequential methods Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Katsumasa Nishide  and
L. C. G. Rogers
Katsumasa Nishide*
Affiliation:
Yokohama National University
L. C. G. Rogers*
Affiliation:
University of Cambridge
*
∗Postal address: International Graduate School of Social Sciences, Yokohama National University, Yokohama 240-8501, Japan. Email address: [email protected]
∗∗Postal address: Statistical Laboratory, University of Cambridge, Cambridge CB3 0WB, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present simple extensions of earlier works on the optimal time to exchange one basket of log Brownian assets for another. A superset and subset of the optimal stopping region in the case where both baskets consist of multiple assets are obtained. It is also shown that a conjecture of Hu and Øksendal (1998) is false except in the trivial case where all the assets in a basket are the same processes.

Keywords

Log Brownian motionoptimal stopping timecontinuation regionconvex hull

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 62L15: Optimal stopping 93E20: Optimal stochastic control
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 21 - 30
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Christensen, S. and Irle, A. (2011). A harmonic-function technique for the optimal stopping diffusions. To appear in Stochastics.Google Scholar
[2] Hu, Y. and Øksendal, B. (1998). Optimal time to invest when the price processes are geometric Brownian motions. Finance Stoch. 2, 295–310.Google Scholar
[3] McDonald, R. and Siegel, D. (1986). The value of waiting to invest. Quart. J. Econom. 101, 707–728.Google Scholar
[4] Olsen, T. E. and Stensland, G. (1992). On optimal timing of investment when cost components are additive and follow geometric Brownian diffusions. J. Econom. Dynamics Control 16, 39–51.CrossRefGoogle Scholar