Modeling and predicting IBNR reserve: extended chain ladder and heteroscedastic regression analysis

Costa, Leonardo Silva da; Pizzinga, Adrian; Atherino, Rodrigo

doi:10.1080/02664763.2015.1079305

Cited by 5 publications

(22 citation statements)

References 10 publications

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“…so that it avoids naturally the problem of the logarithmic transformation of negative incremental values. One can characterize it as the CL approach with dynamic changes of the development factors by the random walk mechanism (for the stochastic model underlying the CL technique see, e.g., Costa et al (2016), Mack (1993), or Renshaw and Verrall (1998)). The corresponding linear Gaussian SSM (with mutually independent residuals ε and η) can be written either in the double-index format for i = 0, .…”

Section: Chain Ladder Ssm (Iii)mentioning

confidence: 99%

Applying State Space Models to Stochastic Claims Reserving

Hendrych¹,

Cipra²

2020

ASTIN Bull.

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The paper solves the loss reserving problem using Kalman recursions in linear statespace models. In particular, if one orders claims data from run-off triangles to time series with missing observations, then state space formulation can be applied for projections or interpolations of IBNR (Incurred But Not Reported) reserves. Namely, outputs of the corresponding Kalman recursion algorithms for missing or future observations can be taken as the IBNR projections. In particular, by means of such recursive procedures one can perform effectively simulations in order to estimate numerically the distribution of IBNR claims which may be very useful in terms of setting and/or monitoring of prudency level of loss reserves. Moreover, one can generalize this approach to the multivariate case of several dependent run-off triangles for correlated business lines and the outliers in claims data can be also treated effectively in this way. Results of a numerical study for several sets of claims data (univariate and multivariate ones) are presented.

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Section: Chain Ladder Ssm (Iii)mentioning

confidence: 99%

Applying State Space Models to Stochastic Claims Reserving

Hendrych¹,

Cipra²

2020

ASTIN Bull.

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“…It is also possible to consider a tail effect for rows beyond the actual year J, which are portrayed in Figure 1 by the shaded observations for which i goes from J+1 to J +m and j initiates at 0 and goes up to J+n. Such extension, proposed by Costa et al (2016), corresponds to "future" IBNR data: reserves for accidents that will occur in J+1,J+2,… and might not be immediately reported.…”

Section: The Runoff Triangle and Ibnr Reservesmentioning

confidence: 99%

“…In this section we employ the methods of Section 4 with a real runoff triangle, which has been frequently analyzed in the literature; see, for example, Taylor and Ashe (1983), Verrall (1989), Mack (1993), Atherino et al (2010), andCosta et al (2016). This is shown in Figure 4.…”

Section: Applicationmentioning

confidence: 99%

“…The contribution of this paper to Atherino et al is twofold. First, we extend the Atherino et al paradigm to consider a calendar year IBNR reserve prediction, which, as discussed by Costa et al (2016), is a key to an insurance company for making short-term IBNR reserves. Second, we add tail effects to the runoff triangle in the linear state model equations, so as to make the IBNR estimation more conservative and thus more effective to protect insurance companies from insolvency risks.…”

Section: Introductionmentioning

confidence: 99%

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State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

Costa

Pizzinga

2019

Journal of Forecasting

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The issue of modeling and forecasting IBNR (incurred but not reported) actuarial reserve under Kalman filter techniques and extensions, using data arranged in a runoff triangle, is a frequent theme in the literature. One quite recent approach is to order the runoff triangle under a row-wise fashion and use linear state-space models for the resulting data set. To allow new possibilities for short-term IBNR reserves as well as to mitigate insolvency risk, in this paper we extend such a state-space method by: (i) a calendar year IBNR reserve prediction; and (ii) a tail effect for the row-wise ordered triangle. The extension is implemented with a real runoff triangle and compared with some traditional IBNR predictors. Empirical results indicate that the approach of this paper outperforms the competing methods in terms of out-of-sample comparisons and gives more conservative IBNR reserves than the original statespace method.

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“…In insurance, state‐space modelling for estimating incurred‐but‐not‐reported (IBNR) reserves (cf. de Jong and Zehnwirth, 1983; Taylor, 2000; Atherino et al, 2010; Grize, 2015; Costa et al, 2016) typically involves predicting non‐standard affine functions of the state vector, so that calculating the corresponding mean squared errors is very hard. In quantitative finance, applying state‐space methods for pairs‐trading strategies (cf.…”

Section: Introductionmentioning

confidence: 99%

Extensions to the invariance property of maximum likelihood estimation for affine‐transformed state‐space models

Pizzinga¹,

Fernandes²

2020

Journal Time Series Analysis

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Replacing the state vector of a linear state‐space model by any one‐to‐one linear transformation does not alter maximum likelihood estimation. We extend this invariance property to more general settings, with possibly diffuse initialization of the Kalman filter and injective affine transformations of the state vector. Our results hold for both direct maximization of the likelihood function and the EM algorithm. We offer two real examples that illustrate how one may employ our results to handle a variety of affine‐transformed state‐space models in the literature.

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Modeling and predicting IBNR reserve: extended chain ladder and heteroscedastic regression analysis

Cited by 5 publications

References 10 publications

Applying State Space Models to Stochastic Claims Reserving

Applying State Space Models to Stochastic Claims Reserving

State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects

Extensions to the invariance property of maximum likelihood estimation for affine‐transformed state‐space models

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