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Constant barrier strategies in a two-state Markov-modulated dual risk model. (English) Zbl 1268.91171

Summary: We consider the dividend problem in a two-state Markov-modulated dual risk model, in which the gain arrivals, gain sizes and expenses are influenced by a Markov process. A system of integro-differential equations for the expected value of the discounted dividends until ruin is derived. In the case of exponential gain sizes, the equations are solved and the best barrier is obtained via a numerical example. Finally, using this example, we compare the best barrier and the expected discounted dividends in the two-state Markov-modulated dual risk model with those in an associated averaged compound Poisson risk model. Numerical results suggest that one could use the results of the associated averaged compound Poisson risk model to approximate those for the two-state Markov-modulated dual risk model.

MSC:

91G50 Corporate finance (dividends, real options, etc.)
60J05 Discrete-time Markov processes on general state spaces
60J22 Computational methods in Markov chains
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
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