Optimal Dynamic Ruin Probabilities for Heavy-Tailed Losses Under Reinsurance Strategies

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Yildirim Külekci B., Korn R., Kestel A. S.

25th (2022) International Congress on Insurance: Mathematics and Economics, Guangzhou, Çin, 12 - 15 Temmuz 2022, cilt.1, ss.114

  • Yayın Türü: Bildiri / Özet Bildiri
  • Cilt numarası: 1
  • Basıldığı Şehir: Guangzhou
  • Basıldığı Ülke: Çin
  • Sayfa Sayıları: ss.114
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In recent years, extreme events are appearing to increase both in frequency and severity in many different areas. Insurance mechanism provides safe protection for extreme losses in the frame of risk management solutions. Reinsurance agreements that insurance companies apply to manage heavy-tailed risks and create free capital are also directly affected by these extreme events. Therefore, we first model the heavy-tailed loss distributions by using the dynamic EVT-GARCH combined model to fit the specific features of heavy-tailed and skewed insurance data and provide more accurate estimates than the classical models considering the structural changes in data. Secondly, we examine the effects of reinsurance strategies on the asymptotic probability of ruin of the Cramér-Lundberg risk process. With numerical examples, we aim to illustrate the optimal reinsurance strategy for the insurer and the reinsurer. Additionally, we derive the corresponding expected value premiums and tail risk measure Value at Risk (VaR) which also allows us to compare these strategies.