The compound binomial model with randomly paying dividends to shareholders and policyholders

Considering surplus of a joint stock insurance company based on compound binomial model, set up thresholds a1, a2 for shareholders and policyholders respectively. When surplus is no less than the thresholds, the company randomly pays dividends to shareholders and policyholders with probabilities q1, q2 respectively. For this model, we have derived the recursive formulas of both the expected discount penalty function and ruin probability, and the distribution function of the deficit at ruin.