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Weak limits of random coefficient autoregressive processes and their application in ruin theory

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  • Dong, Y.
  • Spielmann, J.

Abstract

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein–Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability and the discounted penalty function of the discrete-time process.

Suggested Citation

  • Dong, Y. & Spielmann, J., 2020. "Weak limits of random coefficient autoregressive processes and their application in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 1-11.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:1-11
    DOI: 10.1016/j.insmatheco.2019.12.001
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