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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 748204, 11 pages
http://dx.doi.org/10.1155/2013/748204
Research Article

The Compound Binomial Risk Model with Randomly Charging Premiums and Paying Dividends to Shareholders

School of Business, Central South University, Changsha, Hunan 410083, China

Received 24 October 2012; Revised 22 May 2013; Accepted 4 June 2013

Academic Editor: Samir H. Saker

Copyright © 2013 Xiong Wang and Lei He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based on characteristics of the nonlife joint-stock insurance company, this paper presents a compound binomial risk model that randomizes the premium income on unit time and sets the threshold for paying dividends to shareholders. In this model, the insurance company obtains the insurance policy in unit time with probability and pays dividends to shareholders with probability when the surplus is no less than . We then derive the recursive formulas of the expected discounted penalty function and the asymptotic estimate for it. And we will derive the recursive formulas and asymptotic estimates for the ruin probability and the distribution function of the deficit at ruin. The numerical examples have been shown to illustrate the accuracy of the asymptotic estimations.