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Tail estimates for exponential functionals and applications to SDEs

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  • Nguyen, Tien Dung

Abstract

In this paper, based on techniques of Malliavin calculus, we obtain an explicit bound for tail probabilities of a general class of exponential functionals. We apply the obtained results to derive asymptotic behaviors for the tail of the exponential functional of stochastic differential equations.

Suggested Citation

  • Nguyen, Tien Dung, 2018. "Tail estimates for exponential functionals and applications to SDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4154-4170.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:12:p:4154-4170
    DOI: 10.1016/j.spa.2018.02.003
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    References listed on IDEAS

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    1. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Representation formulas for Malliavin derivatives of diffusion processes," Finance and Stochastics, Springer, vol. 9(3), pages 349-367, July.
    2. Kohatsu-Higa, Arturo & Makhlouf, Azmi, 2013. "Estimates for the density of functionals of SDEs with irregular drift," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1716-1728.
    3. Dung, Nguyen Tien, 2016. "Tail probability estimates for additive functionals," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 349-356.
    4. M. Dozzi & E. T. Kolkovska & J. A. López-Mimbela, 2014. "Finite-Time Blowup and Existence of Global Positive Solutions of a Semi-linear Stochastic Partial Differential Equation with Fractional Noise," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 95-108, Springer.
    5. Dung, Nguyen Tien, 2016. "Tail probabilities of solutions to a generalized Ait-Sahalia interest rate model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 98-104.
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