## Level-crossing properties of the risk process

DC FieldValueLanguage
dc.date.accessioned2021-12-23T16:04:31Z-
dc.date.available2021-12-23T16:04:31Z-
dc.date.issued1998
dc.identifier.issn0364765X
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/6463-
dc.description.abstractFor the classical risk process R(t) that is linear increasing with slope 1 between downward jumps of i.i.d. random sizes at the points of a homogeneous Poisson process we consider the level-crossing process C(x) = (L(x), (Ai(x), B-i (x))(1 less than or equal to i less than or equal to L(x))), where L(x) is the number of jumps from (X, infinity) to (-infinity, x) and A(i)(x) (B-i(x)) are the distances from x to R(t) after (before) the i th jump of this kind. It is shown that if R() has a drift toward infinity, C() is a stationary Markov process; its transition probabilities are determined. As an application we derive the expected value E(L(x)L(x y)).
dc.language.isoen
dc.publisherINST OPERATIONS RESEARCH MANAGEMENT SCIENCES
dc.relation.ispartofMATHEMATICS OF OPERATIONS RESEARCH
dc.subjectMathematics
dc.subjectMathematics, Applied
dc.subjectOperations Research & Management Science
dc.subjectrisk process
dc.subjectstationary Markov process
dc.titleLevel-crossing properties of the risk process
dc.typejournal article
dc.identifier.doi10.1287/moor.23.3.576
dc.identifier.isiISI:000078441200004
dc.description.volume23
dc.description.issue3
dc.description.startpage576
dc.description.endpage584
dc.publisher.place901 ELKRIDGE LANDING RD, STE 400, LINTHICUM HTS, MD 21090-2909 USA
dcterms.isPartOf.abbreviationMath. Oper. Res.
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidStWo325-

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