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A note on the condition of no unbounded profit with bounded risk
Finance and stochastics, 2014-04, Vol.18 (2), p.393-405
[Peer Reviewed Journal]
Springer-Verlag Berlin Heidelberg 2014 ;ISSN: 0949-2984 ;EISSN: 1432-1122 ;DOI: 10.1007/s00780-014-0229-8
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Title:
A note on the condition of no unbounded profit with bounded risk
Author:
Takaoka, Koichiro
;
Schweizer, Martin
Subjects:
Arbitrage
;
Asset pricing
;
Economic Theory/Quantitative
Economics
/Mathematical Methods
;
Economics
;
Equivalence
;
Finance
;
Financial services
;
Insurance
;
Integrals
;
Investment policy
;
Management
;
Martingale
;
Mathematics
;
Mathematics and Statistics
;
Probability
;
Probability Theory and Stochastic Processes
;
Profit
;
Profits
;
Quantitative Finance
;
Random variables
;
Risk
;
Risk assessment
;
Statistics for
Business
;
Studies
;
Theorems
Is Part Of:
Finance and stochastics, 2014-04, Vol.18 (2), p.393-405
Description:
As a corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463–520, 1994 ; Stoch. Stoch. Rep. 53:213–226, 1995 ; Math. Ann. 312:215–250, 1998 ), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict sigma-martingale density. This generalizes the continuous-path result of Choulli and Stricker (Séminaire de Probabilités XXX, pp. 12–23, 1996 ) to the càdlàg case and extends the recent one-dimensional result of Kardaras (Finance and Stochastics 16:651–667, 2012 ) to the multidimensional case. It also refines partially the second main result of Karatzas and Kardaras (Finance Stoch. 11:447–493, 2007 ) concerning the existence of an equivalent supermartingale deflator. The proof uses the technique of numéraire change.
Publisher:
Berlin/Heidelberg: Springer Berlin Heidelberg
Language:
English
Identifier:
ISSN: 0949-2984
EISSN: 1432-1122
DOI: 10.1007/s00780-014-0229-8
Source:
Alma/SFX Local Collection
ProQuest Central
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