A note on the uniform asymptotic behavior of the finite-time ruin probability in a nonstandard renewal risk model

Abstract

Consider a nonstandard renewal risk model in which claims and interarrival times form a sequence of independent and identically distributed random pairs, with each pair obeying arbitrary dependence or size-dependence structure. In the case of heavy-tailed claims, we obtain the asymptotic behavior of finite-time ruin probability with the uniformity in time in some infinite regions.

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Correspondence to Yang Yang.

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The research was supported by the National Natural Science Foundation of China (No. 71471090), Natural Science Foundation of the Jiangsu Higher Education Institutions (No. 19KJA180003), PAPD, the High Level Talent Project of Six Talents Peak of Jiangsu Province (No. JY-039), the Project of Construction for Superior Subjects of Mathematics/Statistics of Jiangsu Higher Education Institutions.

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Cang, Y., Yang, Y. & Shi, X. A note on the uniform asymptotic behavior of the finite-time ruin probability in a nonstandard renewal risk model. Lith Math J 60, 161–172 (2020). https://doi.org/10.1007/s10986-020-09473-x

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Keywords

  • non-standard renewal risk model
  • finite-time ruin probability
  • asymptotics
  • size-dependence
  • heavy tail
  • uniformity

MSC

  • 62P05
  • 62E20
  • 91B30