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Martingale Approach to Derive Lundberg-Type Inequalities

Author

Listed:
  • Tautvydas Kuras

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    All authors contributed equally to this work.)

  • Jonas Sprindys

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    All authors contributed equally to this work.)

  • Jonas Šiaulys

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    All authors contributed equally to this work.)

Abstract

In this paper, we find the upper bound for the tail probability P sup n ⩾ 0 ∑ I = 1 n ξ I > x with random summands ξ 1 , ξ 2 , … having light-tailed distributions. We find conditions under which the tail probability of supremum of sums can be estimated by quantity ϱ 1 exp { − ϱ 2 x } with some positive constants ϱ 1 and ϱ 2 . For the proof we use the martingale approach together with the fundamental Wald’s identity. As the application we derive a few Lundberg-type inequalities for the ultimate ruin probability of the inhomogeneous renewal risk model.

Suggested Citation

  • Tautvydas Kuras & Jonas Sprindys & Jonas Šiaulys, 2020. "Martingale Approach to Derive Lundberg-Type Inequalities," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1742-:d:426123
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    References listed on IDEAS

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