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Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk of ruin there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included.