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Gambling theory and stock option models

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Gambling theory and stock option models
Identifier
ETD_2138
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000052014
Language
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Statistics
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Games of chance (Mathematics)
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Stochastic models
Abstract
This thesis investigates problems both in gambling theory and in stock option
models. In gambling theory, we study the difference between the Vardi casino
and the Dubins-Savage casino. In the simple Dubins-Savage casino there is only
one table in which a sub-fair gamble is available fixed odds ratio, r and the problem
is to change a fortune of size f to a fortune of size 1 with maximum probability
before going broke. Vardi proposed the casino where there is available a table for
each odds ratio r. Since the Dubins-Savage casino can be duplicated in the Vardi
casino, it is clear that the Vardi casino will provide a bigger probability to achieve
the goal than the Dubins-Savage casino. A main result of the thesis is to show
that the advantage of the Vardi casino is surprisingly small. This implies the
surprising conclusion that it does not really help the gambler to have a variety
of gambles available, and raises the question of why casinos in the real world
have such a variety of gambles. In particular, the optimal probabilities of the
Vardi casino and the Dubins-Savage casino with odds ratio r = 1 (red-and-black)
agree to three decimal places. We further conjecture that the largest difference between the Vardi and the Dubins-Savage optimal probabilities occurs at f =
1/3. The thesis also studies the two classic stochastic models involved in finance
and economics, the additive Bachelier model and the multiplicative Black-scholes
model. Both models have advantages and shortcomings. Chen et al [6] introduced
a general class of models with decreasing-return- to-scale indexed by a parameter
interpolating between the additive (θ= 0) and the multiplicative (θ= 1) cases.
We study the American and the Russian option under the decreasing-return-to-
scale models and give the optimal policy of each option for these new models.
The two parts of the thesis are related through the fact that gambling is involved
in each case, this despite the fact that investors often prefer to believe there is
no gambling involved in their activity. Of course gamblers often believe this as
well. Furthermore, among the stocks with the same negative drift, in order to
maximize the probability to achieve a particular amount of fortune to survive for
the gamblers problem of stocks (see [29] [30]), they need to buy those stocks with
big volatilities (odds ratios).
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
ix, 39 p. : ill.
InternetMediaType
application/pdf
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text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p.37-38)
Note (type = statement of responsibility)
by Jianxiong Lou
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Lou
NamePart (type = given)
Jianxiong
NamePart (type = date)
1980
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author
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Jianxiong Lou
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Shepp
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Lawrence
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chair
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Advisory Committee
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Lawrence Shepp
Name (ID = NAME-3); (type = personal)
NamePart (type = family)
Zhang
NamePart (type = given)
Cunhui
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internal member
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Advisory Committee
DisplayForm
Cunhui Zhang
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Singh
NamePart (type = given)
Kesar
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internal member
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Advisory Committee
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Kesar Singh
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Ocone
NamePart (type = given)
Daniel
Role
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outside member
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Advisory Committee
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Daniel Ocone
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-10
Location
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NjNbRU
RelatedItem (type = host)
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/T3Q81D89
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
Copyright
Status
Copyright protected
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Lou
GivenName
Jianxiong
Role
Copyright Holder
Telephone
Address
Email
ContactInformationDate
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
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Label
Place
DateTime
2009-10-01 14:11:22
Detail
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Name
Jianxiong Lou
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject (ID = AO-1); (AUTHORITY = rulib)
Type
License
Name
Author Agreement License
Detail
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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ETD
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application/pdf
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application/x-tar
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Checksum (METHOD = SHA1)
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