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Bull. Korean Math. Soc. 2011; 48(2): 325-334

Printed March 1, 2011

https://doi.org/10.4134/BKMS.2011.48.2.325

Copyright © The Korean Mathematical Society.

Asymptotic distribution of the discounted proper deficit in the discrete time delayed renewal model

Zhen-hua Bao and Jing Wang

Liaoning Normal University, Liaoning Normal University

Abstract

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In this paper we consider the discrete time delayed renewal risk model. We investigate what will happen when the distribution function of the discounted proper deficit is asymptotic in the initial surplus. In doing this we establish several lemmas regarding some related ruin quantities in the discrete time delayed renewal risk model, which are of significance on their own right.

Keywords: discrete time delayed renewal risk model, discounted proper distribution of the deficit, probability generating function of ruin time

MSC numbers: 91B30, 62P05

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