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 a 1 , a 2 for shareholders and policyholders respectively. When surplus is no less than the thresholds, the company randomly pays dividends to shareholders and policyholders with probabilities q 1 , q 2 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.