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A cyclic approach on classical ruin model

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  • Yuen, Fei Lung
  • Lee, Wing Yan
  • Fung, Derrick W.H.

Abstract

The ruin problem has long since received much attention in the literature. Under the classical compound Poisson risk model, elegant results have been obtained in the past few decades. We revisit the finite-time ruin probability by using the idea of cycle lemma, which was used in proving the ballot theorem. The finite-time result is then extended to infinite-time horizon by applying the weak law of large numbers. The cycle lemma also motivates us to study the claim instants retrospectively, and this idea can be used to reach the ladder height distribution on the infinite-time horizon. The new proofs in this paper link the classical finite-time and infinite-time ruin results, and give an intuitive way to understand the nature of ruin.

Suggested Citation

  • Yuen, Fei Lung & Lee, Wing Yan & Fung, Derrick W.H., 2020. "A cyclic approach on classical ruin model," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 104-110.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:104-110
    DOI: 10.1016/j.insmatheco.2020.01.005
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    References listed on IDEAS

    as
    1. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 63-84, September.
    2. Konstantopoulos, Takis, 1995. "Ballot theorems revisited," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 331-338, September.
    3. Gerber, Hans U., 1988. "Mathematical fun with ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 15-23, January.
    4. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Ballot theorem; Ruin probability; Stationary and independent increment; Law of large numbers; Deficit at ruin;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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