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Ruin problems with worsening risks or with infinite mean claims

Author

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  • Dominik Kortschak

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Stéphane Loisel

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Pierre Ribereau

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

In this paper, we obtain asymptotic ruin probabilities in two models where claim amounts become more and more adverse, because of phenomena like climate change or some kind of sectorial inflation. The method we use also enables us to study a risk model in which claims have infinite mean. In such models, ruin probability can be controlled by a strong increase in the premium income rate, which causes premium to become unacceptable for customers. We provide numerical illustrations of the impact of the (uncertain) speed of change in the parameter of the claim size distribution, both in terms of ruin and in terms of time at which premium becomes too high.

Suggested Citation

  • Dominik Kortschak & Stéphane Loisel & Pierre Ribereau, 2014. "Ruin problems with worsening risks or with infinite mean claims," Post-Print hal-00735843, HAL.
    • Handle: RePEc:hal:journl:hal-00735843
    Note: View the original document on HAL open archive server: https://hal.science/hal-00735843v1
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    References listed on IDEAS

    as
    1. Søren Asmussen & Romain Biard, 2011. "Ruin probabilities for a regenerative Poisson gap generated risk process," Post-Print hal-00569254, HAL.
    2. Asmussen, Søren & Henriksen, Lotte Fløe & Klüppelberg, Claudia, 1994. "Large claims approximations for risk processes in a Markovian environment," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 29-43, November.
    3. Bargès, Mathieu & Cossette, Hélène & Loisel, Stéphane & Marceau, Étienne, 2011. "On the Moments of Aggregate Discounted Claims with Dependence Introduced by a FGM Copula," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 215-238, May.
    4. Gerber, Hans U., 1974. "On Additive Premium Calculation Principles," ASTIN Bulletin, Cambridge University Press, vol. 7(3), pages 215-222, March.
    5. 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.
    6. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
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