×

zbMATH — the first resource for mathematics

Ruin probabilities of a dual Markov-modulated risk model. (English) Zbl 1292.91100
Summary: This article is devoted to studying a dual Markov-modulated risk model, which can properly represent, to some extent, surplus processes of companies that pay costs continuously and have occasional gains. We consider both the finite and infnite horizon ruin probabilities under this dual model. Upper and lower bounds of Lundberg type are derived for these ruin probabilities. We also obtain a time-dependent version of Lundberg type inequalities.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1142/9789812779311 · doi:10.1142/9789812779311
[2] DOI: 10.1016/j.insmatheco.2006.10.002 · Zbl 1131.91026 · doi:10.1016/j.insmatheco.2006.10.002
[3] Grandell J., Aspects of Risk Theory (1991) · Zbl 0717.62100
[4] DOI: 10.1093/qmath/12.1.283 · Zbl 0101.25302 · doi:10.1093/qmath/12.1.283
[5] Seal H., Stochastic Theory of a Risk Business (1967) · Zbl 0196.23501
[6] Tákacs L., Combinatorial Methods in the Theory of Stochastic Processes (1969)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.