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A stochastic delay financial model
Author(s):
George
Stoica
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1837-1841.
MSC (2000):
Primary 91B28;
Secondary 91B26
Posted:
December 20, 2004
MathSciNet review:
2120285
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Abstract:
We compute the logarithmic utility of an insider when the financial market is modelled by a stochastic delay equation. Although the market does not allow free lunches and is complete, the insider can draw more from his wealth than the regular trader. We also offer an alternative to the anticipating delayed Black-Scholes formula, by proving stability of European call option prices when the delay coefficients approach the nondelayed ones.
References:
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- 1.
- M. Arriojas, Y. Hu, S.-E. Mohammed, G. Pap, A delayed Black and Scholes formula, preprint 2003. Available at: http://salah.math.siu.edu/
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- K. Back, Insider trading in continuous time, Rev. Fin. Stud. 5 (1992), 387-409.
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- F. Delbaen, W. Schachermayer, A general version of the fundamental theorem of asset pricing, Math. Ann. 300 (1994), 463-520. MR 1304434 (95m:90022b)
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- K. Itô, M. Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ. 41 (1964), 1-75. MR 0177456 (31:1719)
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Additional Information:
George
Stoica
Affiliation:
Department of Mathematical Sciences, University of New Brunswick, P.O. Box 5050, Saint John, New Brunswick, Canada E2L 4L5
Email:
stoica@unbsj.ca
DOI:
10.1090/S0002-9939-04-07765-2
PII:
S 0002-9939(04)07765-2
Keywords:
Stochastic delay equation,
maximal logarithmic utility,
insider,
no-arbitrage,
complete market
Received by editor(s):
January 8, 2004
Received by editor(s) in revised form:
February 20, 2004
Posted:
December 20, 2004
Additional Notes:
The first author was supported in part by NSERC Canada Grant \#249730
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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