Minimal martingale measure on a finite probability space
Author:
Vadym Doroshenko
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 84 (2012), 33-42
MSC (2010):
Primary 91G99; Secondary 60G42, 15A06
DOI:
https://doi.org/10.1090/S0094-9000-2012-00852-1
Published electronically:
July 26, 2012
MathSciNet review:
2857414
Full-text PDF Free Access
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Additional Information
Abstract: Necessary and sufficient conditions are established for the existence of a minimal martingale measure for a discrete time financial market on a finite probability space.
References
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- Martin Schweizer, Option hedging for semimartingales, Stochastic Process. Appl. 37 (1991), no. 2, 339–363. MR 1102880, DOI https://doi.org/10.1016/0304-4149%2891%2990053-F
- Hans Föllmer and Martin Schweizer, Hedging of contingent claims under incomplete information, Applied stochastic analysis (London, 1989) Stochastics Monogr., vol. 5, Gordon and Breach, New York, 1991, pp. 389–414. MR 1108430
- Martin Schweizer, On the minimal martingale measure and the Föllmer-Schweizer decomposition, Stochastic Anal. Appl. 13 (1995), no. 5, 573–599. MR 1353193, DOI https://doi.org/10.1080/07362999508809418
- T. Arai, The relations between minimal martingale measure and minimal entropy martingale measure, Asia-Pacific Financial Markets 8 (2001), 137–177.
- F. Biagini and M. Pratelli, Local risk minimization and numéraire, J. Appl. Probab. 36 (1999), no. 4, 1126–1139. MR 1742155, DOI https://doi.org/10.1239/jap/1032374760
- Tahir Choulli and Christophe Stricker, Minimal entropy-Hellinger martingale measure in incomplete markets, Math. Finance 15 (2005), no. 3, 465–490. MR 2147158, DOI https://doi.org/10.1111/j.1467-9965.2005.00229.x
- Aleš Černý and Jan Kallsen, On the structure of general mean-variance hedging strategies, Ann. Probab. 35 (2007), no. 4, 1479–1531. MR 2330978, DOI https://doi.org/10.1214/009117906000000872
- Terence Chan, Pricing contingent claims on stocks driven by Lévy processes, Ann. Appl. Probab. 9 (1999), no. 2, 504–528. MR 1687394, DOI https://doi.org/10.1214/aoap/1029962753
- D. B. Colwell and R. J. Elliott, Discontinuous asset prices and non-attainable contingent claims, Math. Finance 3 (1993), 295–308.
- Hans Föllmer and Alexander Schied, Stochastic finance, Second revised and extended edition, De Gruyter Studies in Mathematics, vol. 27, Walter de Gruyter & Co., Berlin, 2004. An introduction in discrete time. MR 2169807
References
- M. Schweizer, Hedging of Options in a General Semimartingale Model, Diss. ETH Zurich 8615, 1988.
- M. Schweizer, Option hedging for semimartingales, Stoch. Process. Appl. 37 (1991), 339–363. MR 1102880 (92c:90025)
- H. Föllmer and M. Schweizer, Hedging of contingent claims under incomplete information, Applied Stochastic Analysis (M. H. A. Davis and R. J. Elliott, eds.), Stochastics Monographs, vol. 5, Gordon and Breach, New York, 1991, pp. 389–414. MR 1108430 (92g:90029)
- M. Schweizer, On the minimal martingale measure and the Föllmer–Schweizer decomposition, Stoch. Anal. Appl. 13 (1995), 573–599. MR 1353193 (96h:60080)
- T. Arai, The relations between minimal martingale measure and minimal entropy martingale measure, Asia-Pacific Financial Markets 8 (2001), 137–177.
- F. Biagini and M. Pratelli, Local risk minimization and numéraire, J. Appl. Probab. 36 (1999), 1126–1139. MR 1742155 (2001e:91079)
- T. Choulli and C. Stricker, Minimal entropy-Hellinger martingale measure in incomplete markets, Math. Finance 15 (2005), 465–490. MR 2147158 (2006f:91065)
- A. Cerny and J. Kallsen, On the structure of general mean-variance hedging strategies, Ann. Probab. 35 (2007), 1479–1531. MR 2330978 (2009e:60154)
- T. Chan, Pricing contingent claims on stocks driven by Lévy processes, Ann. Appl. Probab. 9 (1999), 504–528. MR 1687394 (2000f:91028)
- D. B. Colwell and R. J. Elliott, Discontinuous asset prices and non-attainable contingent claims, Math. Finance 3 (1993), 295–308.
- H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, 2004. MR 2169807 (2006d:91002)
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Additional Information
Vadym Doroshenko
Affiliation:
Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kyiv 03127, Ukraine
Email:
vadym.doroshenko@gmail.com
Keywords:
Minimal martingale measure,
financial market with discrete time
Received by editor(s):
January 22, 2011
Published electronically:
July 26, 2012
Article copyright:
© Copyright 2012
American Mathematical Society