Minimizing the expected market time to reach a certain wealth level

Kardaras, C; Platen, E

Minimizing the expected market time to reach a certain wealth level

Kardaras, C Platen, E

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Citation:: 2010
Issue Date:: 2010-12-01

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Field	Value	Language
dc.contributor.author	Kardaras, C	en_US
dc.contributor.author	Platen, E https://orcid.org/0000-0003-4595-3123	en_US
dc.date.issued	2010-12-01	en_US
dc.identifier.citation	2010	en_US
dc.identifier.uri	http://hdl.handle.net/10453/36424
dc.description.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 Ĺevy 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. © 2010 Society for Industrial and Applied Mathematics.	en_US
dc.title	Minimizing the expected market time to reach a certain wealth level	en_US
utslib.for	1502 Banking, Finance and Investment	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access

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 Ĺevy 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. © 2010 Society for Industrial and Applied Mathematics.

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http://hdl.handle.net/10453/36424