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Ladder height distributions with marks

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  • Asmussen, Søren
  • Schmidt, Volker

Abstract

For risk processes with a general stationary input, a representation formula of ladder height distributions is proved which includes some additional information on process behaviour at the ladder epoch. The proof is short and probabilistic, and utilizes time reversal, occupation measures and Campbell's formula. The results are applied to stochastic fluid models driven by a general stationary process and the probability is determined that ruin occurs in a given state of the environment.

Suggested Citation

  • Asmussen, Søren & Schmidt, Volker, 1995. "Ladder height distributions with marks," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 105-119, July.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:1:p:105-119
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    References listed on IDEAS

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    1. Asmussen, Søren & Frey, Andreas & Rolski, Tomasz & Schmidt, Volker, 1995. "Does Markov-Modulation Increase the Risk?," ASTIN Bulletin, Cambridge University Press, vol. 25(1), pages 49-66, May.
    2. Offer Kella & Ward Whitt, 1992. "A Storage Model with a Two-State Random Environment," Operations Research, INFORMS, vol. 40(3-supplem), pages 257-262, June.
    3. S. Asmussen & V. Schmidt, 1993. "The ascending ladder height distribution for a certain class of dependent random walks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 47(4), pages 269-277, December.
    4. Dufresne, Francois & Gerber, Hans U., 1988. "The probability and severity of ruin for combinations of exponential claim amount distributions and their translations," Insurance: Mathematics and Economics, Elsevier, vol. 7(2), pages 75-80, April.
    5. Dufresne, Francois & Gerber, Hans U., 1988. "The surpluses immediately before and at ruin, and the amount of the claim causing ruin," Insurance: Mathematics and Economics, Elsevier, vol. 7(3), pages 193-199, October.
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    Cited by:

    1. Schmidli, Hanspeter, 2001. "Distribution of the first ladder height of a stationary risk process perturbed by [alpha]-stable Lévy motion," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 13-20, February.
    2. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    3. Frey, Andreas & Schmidt, Volker, 1996. "Taylor-series expansion for multivariate characteristics of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 1-12, May.

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