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Ruin probabilities with a Markov chain interest model. (English) Zbl 1122.91340
Summary: Finite and infinite time ruin probabilities in a discrete time risk process with a Markov chain interest model are studied. Recursive and integral equations for the ruin probabilities are given. When interest rates are non-negative, generalized Lundberg inequalities for the infinite time ruin probability are derived by inductive and martingale approaches. When interest rates can be negative and loss distributions have regularly varying tails, asymptotic formulas for the finite time ruin probability are given by an inductive approach on the recursive equations.
Reviewer: Reviewer (Berlin)

MSC:
91B30 Risk theory, insurance (MSC2010)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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