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In this paper, we derive the asymptotic estimates for the Gerber-Shiu discounted penalty functions of the risk model with randomly paying dividends to shareholders and policyholders in [4] by constructing renewal equations. For the model, the asymptotic estimates for the ruin probability are obtained, which is a power function. Numerical examples show the effectiveness of the asymptotic estimates.

The Asymptotic Estimates of Discounted Penalty Functions in a Risk Model with Random Paying Dividends to Shareholders and Policyholders