Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Sufficient Poisson jump diffusion market models revisited

Author: Gheorghe Stoica
Journal: Proc. Amer. Math. Soc. 130 (2002), 819-824
MSC (2000): Primary 91B26, 91B70; Secondary 60G44, 60J75
Published electronically: June 21, 2001
MathSciNet review: 1866037
Full-text PDF

Abstract | References | Similar Articles | Additional Information


Motivated by financial market modeling with spike-like jumps spot prices, we present a simple characterisation of the complete two-dimensional Poisson jump-diffusion market models with possibly discontinuous and degenerate coefficients, extending the standard no-arbitrage and completeness working hypothesis for such markets.

References [Enhancements On Off] (What's this?)

  • 1. K.K. Aase, Contingent claims valuation when the security price is a combination of an Itô process and a random point process, Stoch. Proc. Appl. 28 (1988), 185-220. MR 89k:90015
  • 2. I. Bardhan and X. Chao, On martingale measures when asset returns have unpredictable jumps, Stoch. Proc. Appl. 63 (1996), 35-54. MR 97k:90014
  • 3. H. Bühlmann, F. Delbaen, P. Embrechts, and A.N. Shiryaev, No-arbitrage, change of measure and conditional Esscher transforms, CWI Quarterly 9 (1996), 291-317. MR 98h:90015
  • 4. T. Chan, Pricing contingent claims on stocks driven by Lévy processes, Ann. Appl. Prob. 9 (1999), 504-528. MR 2000f:91028
  • 5. D.B. Colwell and R.J. Elliott, Discontinuous asset prices and non-attainable contingent claims, Math. Finance 3 (1993), 295-308.
  • 6. M. Dritschel and P. Protter, Complete markets with discontinuous security price, Finance and Stochastics 3 (1999), 203-214.
  • 7. R.A. Jarrow, X. Jin, and D.B. Madan, The second fundamental theorem of asset pricing, Math. Finance 9 (1999), 255-273.
  • 8. M. Jeanblanc and N. Privault, A complete market model with Poisson and Brownian components, in: Seminar on Stoch. Analysis, Random Fields and Appl., Ascona, 1999 (to appear).
  • 9. M. Jeanblanc-Picqué and M. Pontier, Optimal portfolio for a small investor in a market model with discontinuous prices, Appl. Math. Optim. 22 (1990), 287-310. MR 91k:90050

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 91B26, 91B70, 60G44, 60J75

Retrieve articles in all journals with MSC (2000): 91B26, 91B70, 60G44, 60J75

Additional Information

Gheorghe Stoica
Affiliation: MITACS Centre of Excellence, and Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
Address at time of publication: Department of Mathematics, Statistics and Computer Science, University of New Brunswick, PO Box 5050, Saint John, New Brunswick, Canada E2L 4L5

Received by editor(s): February 16, 2000
Received by editor(s) in revised form: August 11, 2000
Published electronically: June 21, 2001
Additional Notes: The author is indebted to an anonymous referee and to the Probability Editor, whose remarks improved the present version of the note.
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society