In this paper a discrete-time reserve process with a fixed barrier is presented and modelled as a discounted Markov Decision Process. The non-payment of dividends is penalized. The minimization of this penalty results in an optimal control problem. This work focuses on determining the sequence of premiums that minimize penalty costs, and obtaining a rate for the probability of ruin to ensure a sustainable reserve operation. RATES FOR RUIN PROBABILITY This section presents a rate for ruin

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... lity which permits to determine a period of sustainability for the company under the optimum reserve process, that is, the process under the optimal policy (premium) f * (·) ≡ M,