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Viscosity Characterizations of Explosions and Arbitrage.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Viscosity Characterizations of Explosions and Arbitrage./
Author:	Wang, Yinghui.
Description:	1 online resource (101 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-08(E), Section: B.
Contained By:	Dissertation Abstracts International77-08B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781339597706

Viscosity Characterizations of Explosions and Arbitrage.
Wang, Yinghui.

Viscosity Characterizations of Explosions and Arbitrage. - 1 online resource (101 pages)

Source: Dissertation Abstracts International, Volume: 77-08(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis analyzes the viscosity characterizations of the explosion time distribution for diffusions and of the arbitrage function in an equity market model with uncertainty.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781339597706Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Viscosity Characterizations of Explosions and Arbitrage.
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100 1 $a Wang, Yinghui. $3 1179053
245 1 0 $a Viscosity Characterizations of Explosions and Arbitrage.
264 0 $c 2016
300 $a 1 online resource (101 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 77-08(E), Section: B.
500 $a Adviser: Ioannis Karatzas.
502 $a Thesis (Ph.D.) $c Columbia University $d 2016.
504 $a Includes bibliographical references
520 $a This thesis analyzes the viscosity characterizations of the explosion time distribution for diffusions and of the arbitrage function in an equity market model with uncertainty.
520 $a In the first part, we show that the tail distribution U of the explosion time for a multidimensional diffusion --- and more generally, a suitable function U of the Feynman-Kac type involving the explosion time --- is a viscosity solution of an associated parabolic partial differential equation (PDE), provided that the dispersion and drift coefficients of the diffusion are continuous. This generalizes a result of Karatzas and Ruf (2015), who characterize U as a classical solution of a Cauchy problem for the PDE in the one-dimensional case, under the stronger condition of local Holder continuity on the coefficients. We also extend their result to U in the one-dimensional case by establishing the joint continuity of U. Furthermore, we show that U is dominated by any nonnegative classical supersolution of this Cauchy problem. Finally, we consider another notion of weak solvability, that of the distributional (sub/super)solution, and show that U is no greater than any nonnegative distributional supersolution of the relevant PDE.
520 $a In the second part, a more elaborate mathematical finance setting is taken. We show that, in an equity market model with Knightian uncertainty regarding the relative risk and covariance structure of its assets, the arbitrage function --- defined as the reciprocal of the highest return on investment that can be achieved relative to the market using nonanticipative strategies, and under any admissible market model configuration --- is a viscosity solution of an associated Hamilton-Jacobi-Bellman (HJB) equation under appropriate boundedness, continuity and Markovian assumptions on the uncertainty structure. This result generalizes that of Fernholz and Karatzas (2011), who characterized this arbitrage function as a classical solution of a Cauchy problem for this HJB equation under much stronger conditions than those needed here. Our approach and results also extend to the Markovian Market Weight model introduced in Fernholz and Karatzas (2010b).
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Finance. $3 559073
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0508
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Columbia University. $b Mathematics. $3 1179054
773 0 $t Dissertation Abstracts International $g 77-08B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10092272 $z click for full text (PQDT)