On the Application of Random Walk With Delay and Pareto Distributed Interference of Chance To an Insurance Model

Abstract

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.

[Kesemen, Tulay] Karadeniz Tech Univ, Fac Sci, Dept Math, TR-61080 Trabzon, Turkey; [Kucuk, Zafer] Karadeniz Tech Univ, Fac Sci, Dept Stat & Comp Sci, TR-61080 Trabzon, Turkey; [Khaniyev, Tahir] TOBB Univ Econ & Technol, Dept Ind Engn, TR-06560 Ankara, Turkey; [Yetim, Fuat] Karadeniz Tech Univ, Dept Mech & Metall Technol, Abdullah Kanca Vocat Jr Coll, Trabzon, Turkey; [Bektas Kamislik, Ash] Recep Tayyip Erdogan Univ, Fac Arts & Sci, Dept Math, TR-53020 Rize, Turkey