Refinements of bounds for tails of compound distributions and ruin probabilities

Stathis Chadjiconstantinidis and Panos Xenos

Applied Mathematics and Computation, 2022, vol. 421, issue C

Abstract: In this paper we derive lower bounds for right-tails of compound geometric distributions and ruin probabilities in the classical compound Poisson risk model in the heavy-tailed cases using the truncated Lundberg condition, which improve all the corresponding known lower bounds. Some upper bounds are also derived. Examples are given and numerical comparison for ruin probabilities when the adjustment coefficient does not exist are also considered, illustrating the effectiveness of the proposed new bounds. In addition, several bounds for tails of negative binomial distributions are obtained in terms of the tail of compound geometric distributions as well as bounds in the heavy-tailed cases. Also, some bounds for the stop-loss premium associated with compound negative binomial distributions are given. Using Chernoff's upper bounds we derive two-sided bounds for tails of compound Poisson distributions. Finally, two-sided bounds are given for tails of compound logarithmic distributions in the heavy-tailed cases.

Keywords: Compound distribution; Heavy-tailed distribution; Compound geometric distribution; Compound negative binomial distribution; Compound Poisson distribution; Compound logarithmic distribution; Adjustment coefficient; Truncated Cramér-Lundberg condition (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000340

DOI: 10.1016/j.amc.2022.126948

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