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Inequalities for the ruin probability in a controlled discrete-time risk process. (English) Zbl 1189.91071
This paper studies an insurance model where risk process can be controlled by proportional reinsurance. The performance criterion is to choose reinsurance control strategies to bound the ruin probability of a discrete-time process with Markov chain interest. 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.

MSC:
91B30 Risk theory, insurance (MSC2010)
60J05 Discrete-time Markov processes on general state spaces
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