An estimate of ruin probabilities for long range dependence models
Author:
Yulia Mishura
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 72 (2006), 103-111
MSC (2000):
Primary 60H10, 91B30; Secondary 60G44, 60G15
DOI:
https://doi.org/10.1090/S0094-9000-06-00668-5
Published electronically:
August 18, 2006
MathSciNet review:
2168140
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We obtain an estimate of the ruin probability for the case where a company buys a risky asset (security) that is a semimartingale with absolutely continuous characteristics with respect to the Lebesgue measure. This result is applied to some long range dependence models, in particular to the fractional Brownian motion and mixed models.
References
- J. Gaier, P. Grandits, and W. Schachermayer, Asymptotic ruin probabilities and optimal investment, Ann. Appl. Probab. 13 (2003), no. 3, 1054–1076. MR 1994044, DOI https://doi.org/10.1214/aoap/1060202834
- P. Cheridito, Regularizing Fractional Brownian Motion With a View Towards Stock Price Modelling, Ph.D. Thesis, ETH, Zürich, 2001.
- M. Zähle, Integration with respect to fractal functions and stochastic calculus. I, Probab. Theory Related Fields 111 (1998), no. 3, 333–374. MR 1640795, DOI https://doi.org/10.1007/s004400050171
- M. Zähle, Integration with respect to fractal functions and stochastic calculus. I, Probab. Theory Related Fields 111 (1998), no. 3, 333–374. MR 1640795, DOI https://doi.org/10.1007/s004400050171
- A. N. Shiryaev, On arbitrage and replication for fractal models, Research Report, vol. 20, MaPhySto, 1998.
References
- I. Gaier, P. Grandits, and W. Schachermayer, Asymptotic ruin probabilities and optimal investment, Ann. Appl. Probab. 13 (2003), no. 3, 1054–1076. MR 1994044 (2004k:91124)
- P. Cheridito, Regularizing Fractional Brownian Motion With a View Towards Stock Price Modelling, Ph.D. Thesis, ETH, Zürich, 2001.
- M. Zähle, Integration with respect to fractal functions and stochastic calculus I, Prob. Theory Related Fields 111 (1998), 333–374. MR 1640795 (99j:60073)
- I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli 5 (1999), no. 4, 571–587. MR 1640795 (99j:60073)
- A. N. Shiryaev, On arbitrage and replication for fractal models, Research Report, vol. 20, MaPhySto, 1998.
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
60H10,
91B30,
60G44,
60G15
Retrieve articles in all journals
with MSC (2000):
60H10,
91B30,
60G44,
60G15
Additional Information
Yulia Mishura
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
myus@univ.kiev.ua
Received by editor(s):
March 12, 2004
Published electronically:
August 18, 2006
Additional Notes:
Supported by grant PST.CLG.980408.
Article copyright:
© Copyright 2006
American Mathematical Society
