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

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 $x$ for paying dividends to shareholders. In this model, the insurance company obtains the insurance policy in unit time with probability $p_{\mathrm{0}}$ and pays dividends to shareholders with probability $p_{\mathrm{1}}$ when the surplus is no less than $x$. 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.