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Upper bounds on the expected time to ruin and on the expected recovery time. (English) Zbl 1123.91335
Summary: It is shown that the time to ruin and the recovery time in a risk process have the same distribution as the busy period in a certain queueing system. Similarly, the deficit at the time of ruin is distributed as the idle period in a single-server queueing system. These duality results are exploited to derive upper bounds for the expected time to ruin and the expected recovery time as defined by EgĂ­dio dos Reis (2000). When the claim size is generally distributed, Lorden’s inequality is applied to derive the bounds. When the claim-size distribution is of phase type, tighter upper bounds are derived.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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