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Mean-risk portfolio optimization problems with risk-adjusted measures

## Descriptive

TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Mean-risk portfolio optimization problems with risk-adjusted measures
SubTitle
PartName
PartNumber
NonSort
Identifier
ETD_1247
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000050460
Language (objectPart = )
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Operations Research
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Portfolio management--Mathematical models
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Risk
Abstract
We consider the problem of optimizing a portfolio of finitely many assets whose returns are described by a joint discrete distribution. We formulate the mean-risk model, using as risk functions the semi deviation and weighted deviation from quantile. Using representation theorems from convex analysis, we write the portfolio problem equivalently as a zero-sum matrix game, and provide convex optimization techniques for its solution. A new set of risk-adjusted probability measures is derived from the optimal saddle point solution of the game. The risk-adjusted probability measures can be used to evaluate portfolio performance. An illustrative example is provided in which these measures are derived for a portfolio of 200 assets, and are used to evaluate a market portfolio and optimal risk-averse portfolio. The results suggest the mean-risk portfolio is more robust than a market portfolio. We extend the above mean-risk model to the two-stage portfolio problem, where there are two investment periods and the option to rebalance in between. The resulting model is a two-stage stochastic programming problem, with mean-risk objectives in each stage. First and second stage risk-adjusted probability measures are derived in a similar fashion to the one investment period problem. Using as risk functions semi deviation and weighted deviation from quantile in both stages, we calculate the risk adjusted measures in a numerical example with 100 assets. These measures are used to evaluate a two-stage market portfolio and optimal risk-averse portfolio. We extend the cutting-plane and multi-cut algorithms for solving linear two-stage stochastic problems to the two-stage mean-risk portfolio problem. The two-stage portfolio problem is also formulated as one large linear program. We provide an illustrative example, where a two-stage portfolio problem with risk functions semi deviation and weighted deviation from quantile is solved, using these two methods and the simplex method. The performance of these three methods is compared for solving the portfolio problem. On large examples, the extended cutting-plane and multi-cut plane algorithms solve where the linear program fails.
PhysicalDescription
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electronic resource
Extent
xiii, 96 p. : ill.
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application/pdf
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text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 93-98)
Note (type = statement of responsibility)
by Naomi Liora Miller
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Miller
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Naomi Liora
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author
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Naomi Liora Miller
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Prekopa
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Andras
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chair
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Andras Prekopa
Name (ID = NAME-3); (type = personal)
NamePart (type = family)
Ruszczynski
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Andrzej
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internal member
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Andrzej Ruszczynski
Name (ID = NAME-4); (type = personal)
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Boros
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Endre
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internal member
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Endre Boros
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Gurvich
NamePart (type = given)
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RoleTerm (authority = RULIB); (type = )
internal member
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DisplayForm
Name (ID = NAME-6); (type = personal)
NamePart (type = family)
Eckstein
NamePart (type = given)
Jonathan
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internal member
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Jonathan Eckstein
Name (ID = NAME-7); (type = personal)
NamePart (type = family)
Dentcheva
NamePart (type = given)
Darinka
Role
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outside member
Affiliation
DisplayForm
Darinka Dentcheva
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB); (type = )
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Role
RoleTerm (authority = RULIB); (type = )
school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2008
DateOther (qualifier = exact); (type = degree)
2008-10
Place
PlaceTerm (type = code)
xx
Location
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NjNbRU
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = doi)
doi:10.7282/T3JD4X37
Genre (authority = ExL-Esploro)
ETD doctoral
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## Rights

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The author owns the copyright to this work.
Status
Availability
Status
Open
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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## Technical

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