ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL

Authors : Zafer KÜÇÜK, Tülay KESEMEN, Tahir KHANİYEV, Fuat YETİM, Aslı BEKTAŞ KAMIŞLIK

Pages : 615-626

View : 21 | Download : 7

Publication Date : 2016-09-30

Article Type : Other Papers

Abstract :In this study, a semi-Markovian random walk insert ignore into journalissuearticles values(Xinsert ignore into journalissuearticles values(t);); with Pareto distributed interference of chance and delay is considered. Some exact formulas for the first four stationary moments of the process Xinsert ignore into journalissuearticles values(t); are obtained, when the random variables $\zetta_n,n=1,2,...$ which express the discrete interference of chance have Pareto distribution with parameters $insert ignore into journalissuearticles values(\alpha, \lamda);$. The random variables $\zetta_n,n=1,2,...$ 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 Xinsert ignore into journalissuearticles values(t); are derived, when $Einsert ignore into journalissuearticles values(zetta_n);$ is sufficiently large. Finally, by using Monte-Carlo simulation method, the accuracy of obtained approximation formulas is tested.
Keywords : Insurance model, random walk with delay, Pareto distribution, asymptotic expansion, Monte Carlo simulation method