A note on the compound binomial model with randomized dividend strategy

This paper considers the compound binomial model with randomized decisions on paying dividends. By using two formulas obtained by Tan and Yang [J.Y. Tan, X.Q. Yang, The compound binomial model with randomized decisions on paying dividends, Insurance: Mathematics and Economics 39 (2006) 1-18], two defective renewal equations for the Gerber-Shiu penalty function are derived and solved. The analytic solutions obtained are utilized to derive the probability of ultimate ruin, the deficit distribution at ruin and the distribution of the claim causing ruin. The asymptotic estimate satisfied by the penalty function is discussed in some detail.