Ruin Probabilities in a Discrete Semi-Markov Risk Model with Random Dividends to Shareholders and Policyholders

The discrete semi-Markov risk model is modified by the inclusion of dividends paying to shareholders and policyholders. When surplus is no less than the thresholds a1 and a2, the company randomly pays dividends to shareholders and policyholders with probabilities q1,q2 respectively. Recursive formulae for ruin probabilities are derived. Finally, a numerical example is given to illustrate the effect of the related parameters on the ruin probabilities.