An individual loss reserving model with independent reporting and settlement

Huang, Jinlong; Qiu, Chunjuan; Wu, X.; Zhou, Xian

doi:10.1016/j.insmatheco.2015.05.010

Cited by 13 publications

(11 citation statements)

References 18 publications

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“…In many situations, the data are recorded chronologically so that the first subscript of reflects the calendar time when the data vector begins to be recorded and the third subscript represents the calendar time that component is recorded; hence the dependence between the data beginning at a same calendar time and independent over calendar times is reasonable. This structure is the typical case of loss reserving in general insurance with individual data (see, e.g., Huang et al [17,18]). …”

Section: Definitionmentioning

confidence: 95%

“…A typical example is loss data for claims used for the purpose of loss reserving in the industry of non-life insurance (see, e.g., [15,17,18]). Assume that the evaluation time of loss reserving is accident year ; each claim made at accident year ( ≤ ) will be paid at the end of the subsequent years after the claim (the first is the one paid at the end of the year the claim is made) so that the payments of an individual ( , ) correspond to a -vector ( 1 , .…”

Section: The Data and Modelmentioning

confidence: 99%

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Estimation of Poisson‐Dirichlet Parameters with Monotone Missing Data

Zhou

Huang²,

2017

Mathematical Problems in Engineering

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This article considers the estimation of the unknown numerical parameters and the density of the base measure in a PoissonDirichlet process prior with grouped monotone missing data. The numerical parameters are estimated by the method of maximum likelihood estimates and the density function is estimated by kernel method. A set of simulations was conducted, which shows that the estimates perform well.

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Section: Definitionmentioning

confidence: 95%

Section: The Data and Modelmentioning

confidence: 99%

Estimation of Poisson‐Dirichlet Parameters with Monotone Missing Data

Zhou

Huang²,

2017

Mathematical Problems in Engineering

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“…We investigate two aggregation levels, namely aggregating based on a yearly as well as a 28 day grid. We refer to Huang et al (2015) for a more detailed discussion on reserving with granular data versus data aggregated in two dimensional tables. Figure 11 shows the estimated IBNR counts under both chain ladder implementations evaluated on each date between September, 2003 andAugust, 2004.…”

Section: Evolution Of the Number Of Hidden Eventsmentioning

confidence: 99%

Modeling the number of hidden events subject to observation delay

Crèvecoeur

Antonio

Verbelen

2019

European Journal of Operational Research

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Copyright © 2019 European Journal of Operational Research. This paper considers the problem of predicting the number of events that have occurred in the past, but which are not yet observed due to a delay. Such delayed events are relevant in predicting the future cost of warranties, pricing maintenance contracts, determining the number of unreported claims in insurance and in modeling the outbreak of diseases. Disregarding these unobserved events results in a systematic underestimation of the event occurrence process. Our approach puts emphasis on modeling the time between the occurrence and observation of the event, the so-called observation delay. We propose a granular model for the heterogeneity in this observation delay based on the occurrence day of the event and on calendar day effects in the observation process, such as weekday and holiday effects. We illustrate this approach on a European general liability insurance data set where the occurrence of an accident is reported to the insurer with delay.

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“…Arjas (1989) and Norberg (1993) formulated models in a classical bio-statistical setup with a non-homogeneous marked Poisson process. A strong case study in this setting has been developed in Antonio & Plat (2014) and the models have been further studied in Huang et al (2015) and Huang et al (2016). These models are more complex than chain-ladder models.…”

Section: Introductionmentioning

confidence: 99%

Continuous chain-ladder with paid data

Bischofberger

Hiabu

Isakson

2019

Scandinavian Actuarial Journal

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We introduce a continuous-time framework for the prediction of outstanding liabilities, in which chain-ladder development factors arise as a histogram estimator of a cost-weighted hazard function running in reversed development time. We use this formulation to show that under our assumptions on the individual data chain-ladder is consistent. Consistency is understood in the sense that both the number of observed claims grows to infinity and the level of aggregation tends to zero. We propose alternatives to chain-ladder development factors by replacing the histogram estimator with kernel smoothers and by estimating a cost-weighted density instead of a cost-weighted hazard. Finally, we provide a real-data example and a simulation study confirming the strengths of the proposed alternatives.We start by putting the unique sampling scheme of chain-ladder into a micro-structure framework. We observe counting processes (N i (t)) t∈[0,T ] , T > 0, for claims i = 1, . . . n and call t development time. Each counting process starts with value zero at the underwriting date underlying its claim. It jumps, with jump-size one, whenever a payment is made. Additionally to every jump, we observe a mark indicating the size of the payment made. The number of counting processes, n, varies over calendar-time: We follow retrospectively only those claims for which at least one payment has been observed, i.e., we do not follow every claim in the policy book. In this paper, we make the following assumptions.[M1] All claims are independent.[M2] Every claim consists of only one payment.Assumptions [M1] and [M2] are rather strong but are made to simplify the mathematical derivations yielding a first and clean step towards a better understanding of chain-ladder on a

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An individual loss reserving model with independent reporting and settlement

Cited by 13 publications

References 18 publications

Estimation of Poisson‐Dirichlet Parameters with Monotone Missing Data

Estimation of Poisson‐Dirichlet Parameters with Monotone Missing Data

Modeling the number of hidden events subject to observation delay

Continuous chain-ladder with paid data

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