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Article Citation - WoS: 11Citation - Scopus: 10Modeling of Claim Exceedances Over Random Thresholds for Related Insurance Portfolios(Elsevier, 2011) Eryilmaz, Serkan; Gebizlioglu, Omer L.; Tank, FatihLarge claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 25Citation - Scopus: 33Dynamic Behavior of k-out-of-n< Systems(Elsevier, 2011) Eryilmaz, SerkanIn this paper, we study the distribution and expected value of the number of working components at time t in usual and weighted k-out-of-n:G systems under the condition that they are working at time t. We evaluate the distribution of the corresponding conditional random variable and compute its expected value for the systems consisting of independent but nonidentical components. Illustrative examples are presented and an optimization problem which makes use of the conditional random variable is also formulated and solved numerically. (c) 2011 Elsevier B.V. All rights reserved.
