A stochastic delay financial model
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- by George Stoica PDF
- Proc. Amer. Math. Soc. 133 (2005), 1837-1841 Request permission
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
- M. Arriojas, Y. Hu, S.-E. Mohammed, G. Pap, A delayed Black and Scholes formula, preprint 2003. Available at: http://salah.math.siu.edu/
- K. Back, Insider trading in continuous time, Rev. Fin. Stud. 5 (1992), 387–409.
- W. Schachermayer, Martingale measures for discrete-time processes with infinite horizon, Math. Finance 4 (1994), no. 1, 25–55. MR 1286705, DOI 10.1111/j.1467-9965.1994.tb00048.x
- Kiyoshi Itô and Makiko Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ. 4 (1964), 1–75. MR 177456, DOI 10.1215/kjm/1250524705
- Igor Pikovsky and Ioannis Karatzas, Anticipative portfolio optimization, Adv. in Appl. Probab. 28 (1996), no. 4, 1095–1122. MR 1418248, DOI 10.2307/1428166
- I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer Verlag, New York-Berlin, 1987.
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
- Received by editor(s): January 8, 2004
- Received by editor(s) in revised form: February 20, 2004
- Published electronically: December 20, 2004
- Additional Notes: The first author was supported in part by NSERC Canada Grant #249730
- Communicated by: Richard C. Bradley
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1837-1841
- MSC (2000): Primary 91B28; Secondary 91B26
- DOI: https://doi.org/10.1090/S0002-9939-04-07765-2
- MathSciNet review: 2120285