On The Application Of Random Walk With Delay And Pareto Distributed Interference Of Chance To An Insurance Model

KESEMEN T., KÜÇÜK Z., Khaniyev T., YETİM F., Bektas Kamislik A.

GAZI UNIVERSITY JOURNAL OF SCIENCE, cilt.29, sa.3, ss.615-626, 2016 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 3
  • Basım Tarihi: 2016
  • Dergi Adı: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.615-626
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this study, a semi-Markovian random walk with Pareto distributed interference of chance and delay is considered. Some exact formulas for the first four stationary moments of the process are obtained when the random variables which express the discrete interference of chance have Pareto distribution with parameters. The random variables are interpreted as loans which insurance company gets from a bank. With the use of these exact formulas, the third-order asymptotic expansions for the first four stationary moments of the process X(t) are derived when is sufficiently large. Finally, by using Monte-Carlo simulation method, the accuracy of the obtained approximation formulas is tested.