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A matrix operator approach to the analysis of ruin-related quantities in the phase-type renewal risk model. (English. German, French summary) Zbl 1333.91025
Summary: It is well-known in ruin theory that the expected present value of penalty at ruin satisfies a defective renewal equation in the Erlang-$$n$$ renewal risk model. This paper presents a new matrix operator approach to derive a parallel defective renewal equation for the expected present value of total operating costs in a phase-type renewal risk model and hence provides explicit matrix analytic solutions to a variety of ruin-related quantities.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 60K05 Renewal theory 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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