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Large deviations for the time-integrated negative parts of some processes

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  • Macci, Claudio

Abstract

In this paper we consider a family of processes which satisfies the large deviation principle with a good rate function; then we prove the large deviation principle for the family of the corresponding time-integrated negative parts, with the application of the so-called contraction principle. An explicit expression of the rate function is presented for a class of examples.

Suggested Citation

  • Macci, Claudio, 2008. "Large deviations for the time-integrated negative parts of some processes," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 75-83, January.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:1:p:75-83
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    References listed on IDEAS

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    1. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes and optimal reserve allocation," Post-Print hal-00397289, HAL.
    2. Stéphane Loisel, 2005. "Differentiation of functionals of risk processes and optimal reserve allocation," Post-Print hal-00397290, HAL.
    3. de Acosta, A., 1994. "Large deviations for vector-valued Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 75-115, June.
    4. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
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    Cited by:

    1. Julien Callant & Julien Trufin & Pierre Zuyderhoff, 2022. "Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 595-611, June.
    2. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.

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