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An estimate of ruin probabilities for long range dependence models
Author(s):
Yulia
Mishura
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
103-111.
MSC (2000):
Primary 60H10, 91B30;
Secondary 60G44, 60G15
Posted:
August 18, 2006
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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:
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- 1.
- 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)
- 2.
- P. Cheridito, Regularizing Fractional Brownian Motion With a View Towards Stock Price Modelling, Ph.D. Thesis, ETH, Zürich, 2001.
- 3.
- M. Zähle, Integration with respect to fractal functions and stochastic calculus I, Prob. Theory Related Fields 111 (1998), 333-374. MR 1640795 (99j:60073)
- 4.
- 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)
- 5.
- A. N. Shiryaev, On arbitrage and replication for fractal models, Research Report, vol. 20, MaPhySto, 1998.
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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
DOI:
10.1090/S0094-9000-06-00668-5
PII:
S 0094-9000(06)00668-5
Received by editor(s):
12/MAR/2004
Posted:
August 18, 2006
Additional Notes:
Supported by grant PST.CLG.980408.
Copyright of article:
Copyright
2006,
American Mathematical Society
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