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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: knishide@ynu.ac.jp
∗∗Postal address: Statistical Laboratory, University of Cambridge, Cambridge CB3 0WB, UK.
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Abstract

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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

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