A micro-level claim count model with overdispersion and reporting delays |
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| Institution: | 1. School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW, Sydney NSW 2052, Australia;2. Département de Mathématiques et de Statistique, Université de Montréal, Montréal QC H3T 1J4, Canada;1. Université de Lyon, Université Lyon 1, Institut Camille Jordan ICJ UMR 5208 CNRS, France;2. Université de Lyon, Université Lyon 1, Laboratoire SAF EA2429, France;1. Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada;2. Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada;1. Department of Statistical Sciences, University of Padova, Padova, Italy;2. Istituto per le Applicazioni del Calcolo “Mauro Picone” - CNR, Roma, Italy;3. Centre for Innovation and Leadership in Health Sciences, University of Southampton, Southampton, UK;4. Dipartimento di Scienze Economiche, Politiche e delle Lingue Moderne, Libera Universitá Maria SS. Assunta, Roma, Italy;5. MEMOTEF Department, Sapienza University of Rome, Rome, Italy;1. Department of Mathematics, University of Illinois at Urbana-Champaign, United States;2. Department of Risk Management & Insurance, Georgia State University, United States |
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| Abstract: | The accurate estimation of outstanding liabilities of an insurance company is an essential task. This is to meet regulatory requirements, but also to achieve efficient internal capital management. Over the recent years, there has been increasing interest in the utilisation of insurance data at a more granular level, and to model claims using stochastic processes. So far, this so-called ‘micro-level reserving’ approach has mainly focused on the Poisson process.In this paper, we propose and apply a Cox process approach to model the arrival process and reporting pattern of insurance claims. This allows for over-dispersion and serial dependency in claim counts, which are typical features in real data. We explicitly consider risk exposure and reporting delays, and show how to use our model to predict the numbers of Incurred-But-Not-Reported (IBNR) claims. The model is calibrated and illustrated using real data from the AUSI data set. |
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| Keywords: | Cox process Shot noise Insurance claims counts Markov chain Monte Carlo Filtering |
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