In this paper, we investigate a quota share reinsurance risk modelwhich is an extension of the one introduced in [14]. Assuming thatthe premium incomes and claim amounts take values in nite sets ofnon-negative numbers, we derive the explicit formula for the joint ruinprobability of the insurer and the reinsurer. Moreover, we give upperbounds of ruin probabilities by martingale and inductive methods. Inparticular, we show that there exists a quota share level that minimizesthe joint ruin probability and the upper bound of ruin probability ofeach insurance companies. Finally, a numerical illustration is given.
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