Minimizing the Expected Market Time to Reach a Certain Wealth Level

Constantinos Kardaras and Eckhard Platen ()

No 230, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Ito market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor’s point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.

Keywords: Numeraire portfolio; growth-optimal portfolio; market time; upcrossing; overshoot; exponential Levy markets; Ito markets; semimartingale markets (search for similar items in EconPapers)
Pages: 15 pages
Date: 2008-08-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Published as: Kardaras, C. and Platen, E., 2010, "Minimizing the Expected Market Time to Reach a Certain Wealth Level", SIAM Journal on Financial Mathematics, 1(1), 16-29.

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Related works:
Working Paper: Minimizing the expected market time to reach a certain wealth level (2009)
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