Abstract
Markov decision theory is applied to study the distribution of dividends of a discrete reserve process with a fixed barrier. The non-payment of dividends is penalized through a cost function which implies solving an optimal control problem. Two objective functions are proposed: a discounted cost and an average one. In both cases, the same optimal strategy for the payment of dividends is obtained, which ensures a ruin probability that guarantees a sustainable reserve operation for claims distributed with light or heavy tails.
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Acknowledgements
R. Montes-de-Oca, P. Saavedra, and D. Cruz-Suárez dedicate this article to the memory of their co-worker and co-author of the present work, Gabriel Zacarías-Espinoza, whose sensible death occured on November, 10, 2015.
This work was partially supported by CONACYT (México) and ASCR (Czech Republic) under Grant No. 171396.
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Montes-de-Oca, R., Saavedra, P., Zacarías-Espinoza, G., Cruz-Suárez, D. (2018). Markov Decision Processes Applied to the Payment of Dividends of a Reserve Process. In: Parlier, G., Liberatore, F., Demange, M. (eds) Operations Research and Enterprise Systems. ICORES 2017. Communications in Computer and Information Science, vol 884. Springer, Cham. https://doi.org/10.1007/978-3-319-94767-9_5
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