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A local limit theorem for random walk maxima with heavy tails

  • Asmussen, Søren
  • Kalashnikov, Vladimir
  • Konstantinides, Dimitrios
  • Klüppelberg, Claudia
  • Tsitsiashvili, Gurami
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    For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution [pi] of the maximum has a tail [pi](x,[infinity]) which is asymptotically proportional to . We supplement here this by a local result showing that [pi](x,x+z] is asymptotically proportional to zF(x,[infinity]).

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-452WD5W-5/2/18bf3b94f53def67173bea798c983f44
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 4 (February)
    Pages: 399-404

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:4:p:399-404
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    1. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    2. Kalashnikov, Vladimir & Konstantinides, Dimitrios, 2000. "Ruin under interest force and subexponential claims: a simple treatment," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 145-149, August.
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