ON 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 (X(t)) with Pareto distributed interference of chance and delay is considered. Some exact formulas for the first four stationary moments of the process X(t) are obtained, when the random variables $\zetta_n,n=1,2,...$ which express the discrete interference of chance have Pareto distribution with parameters $(\alpha, \lamda)$. 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 X(t) are derived, when $E(zetta_n)$ 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

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