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Article: Optimal portfolios with regime switching and value-at-risk constraint

TitleOptimal portfolios with regime switching and value-at-risk constraint
Authors
KeywordsDynamic Programming
Maximum Value-At-Risk Constraints
Optimal Portfolio Selection
Regime-Switching
Regime-Switching Hjb Equations
Utility Maximization
Issue Date2010
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 2010, v. 46 n. 6, p. 979-989 How to Cite?
AbstractWe consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes. © 2010 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156256
ISSN
2015 Impact Factor: 3.635
2015 SCImago Journal Rankings: 4.315
ISI Accession Number ID
Funding AgencyGrant Number
RGCPolyU. 5321/07E
Research Committee of The Hong Kong Polytechnic University
Australian Research Council (ARC)DP1096243
HKRGC7017/07P
Funding Information:

The first and second authors are supported by RGC Grant PolyU. 5321/07E and the Research Committee of The Hong Kong Polytechnic University The third author is supported by the Discovery Grant from the Australian Research Council (ARC), (Project No DP1096243) The last author is supported in part by HKRGC Grant No. 7017/07P, HKUCRGC Grants. HKU Strategy Research Theme fund on Computational Sciences. Hung Hing Ying Physical Research Sciences Research Grant The material in this paper was not presented at any conference. This paper was recommended for publication under the direction of Editor Berc Rustem.

References

 

DC FieldValueLanguage
dc.contributor.authorYiu, KFCen_US
dc.contributor.authorLiu, Jen_US
dc.contributor.authorSiu, TKen_US
dc.contributor.authorChing, WKen_US
dc.date.accessioned2012-08-08T08:41:03Z-
dc.date.available2012-08-08T08:41:03Z-
dc.date.issued2010en_US
dc.identifier.citationAutomatica, 2010, v. 46 n. 6, p. 979-989en_US
dc.identifier.issn0005-1098en_US
dc.identifier.urihttp://hdl.handle.net/10722/156256-
dc.description.abstractWe consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes. © 2010 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automaticaen_US
dc.relation.ispartofAutomaticaen_US
dc.subjectDynamic Programmingen_US
dc.subjectMaximum Value-At-Risk Constraintsen_US
dc.subjectOptimal Portfolio Selectionen_US
dc.subjectRegime-Switchingen_US
dc.subjectRegime-Switching Hjb Equationsen_US
dc.subjectUtility Maximizationen_US
dc.titleOptimal portfolios with regime switching and value-at-risk constrainten_US
dc.typeArticleen_US
dc.identifier.emailYiu, KFC:cedric@hkucc.hku.hken_US
dc.identifier.emailChing, WK:wching@hku.hken_US
dc.identifier.authorityYiu, KFC=rp00206en_US
dc.identifier.authorityChing, WK=rp00679en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.automatica.2010.02.027en_US
dc.identifier.scopuseid_2-s2.0-77953130798en_US
dc.identifier.hkuros170468-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77953130798&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume46en_US
dc.identifier.issue6en_US
dc.identifier.spage979en_US
dc.identifier.epage989en_US
dc.identifier.isiWOS:000278675500003-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridYiu, KFC=24802813000en_US
dc.identifier.scopusauthoridLiu, J=35792106700en_US
dc.identifier.scopusauthoridSiu, TK=8655758200en_US
dc.identifier.scopusauthoridChing, WK=13310265500en_US
dc.identifier.citeulike7055506-

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