Aggregate claim estimation using bivariate hidden Markov model

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<title>Aggregate claim estimation using bivariate hidden Markov model</title>
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<namePart>Nukeshtayeva Oflav, Zarina</namePart>
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<namePart>Yozgatligil, Ceylan</namePart>
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<namePart>Sevtap Selcuk-Kestel, A.</namePart>
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<abstract displayLabel="Summary">In this paper, we propose an approach for modeling claim dependence, with the assumption that the claim numbers and the aggregate claim amounts are mutually and serially dependent through an underlying hidden state and can be characterized by a hidden finite state Markov chain using bivariate Hidden Markov Model (BHMM). We construct three different BHMMs, namely PoissonNormal HMM, PoissonGamma HMM, and Negative BinomialGamma HMM, stemming from the most commonly used distributions in insurance studies. Expectation Maximization algorithm is implemented and for the maximization of the state-dependent part of log-likelihood of BHMMs, the estimates are derived analytically. To illustrate the proposed model, motor third-party liability claims in Istanbul, Turkey, are employed in the frame of PoissonNormal HMM under a different number of states. In addition, we derive the forecast distribution, calculate state predictions, and determine the most likely sequence of states. The results indicate that the dependence under indirect factors can be captured in terms of different states, namely low, medium, and high states.</abstract>
<note type="statement of responsibility">Zarina Nukeshtayeva Oflav, Ceylan Yozgatligil, A. Sevtap Selcuk-Kestel</note>
<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080602437">
<topic>Matemática del seguro</topic>
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<subject xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MAPA20080576783">
<topic>Modelo de Markov</topic>
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<topic>Reclamaciones</topic>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
<identifier type="local">MAP20077000420</identifier>
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<text>01/01/2019 Volumen 49 Número 1 - enero 2019 , p. 189-216</text>
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