Stochastic Loss Reserving in Discrete Time: Individual vs. Aggregate Data Models

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

doi:10.1080/03610926.2014.976473

Cited by 16 publications

(14 citation statements)

References 20 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From this perspective, the sufficient statistics for the aggregated model tell us that no information is lost while aggregating. For more on aggregation of "micro" level information, see, for example, Huang et al (2015Huang et al ( , 2016, Charpentier and Pigeon (2016), . (e) Note that the above model can be expressed in terms of the hierarchical model framework presented in Crevecoeur and Antonio (2019), using number of open claims as one of the layers.…”

Section: Data and Notationmentioning

confidence: 99%

“…Hence, since the R ij s will be proportional to the corresponding N ij s (or expectations thereof), R ij /w i can be thought of as the approximate reserve from a single contract. Thus, consistency of R ij /w i has a natural interpretation and is also treated in, for example, Huang et al (2015Huang et al ( , 2016.…”

Section: Comments On Consistency Of Normalised Reservesmentioning

confidence: 99%

See 1 more Smart Citation

A Collective Reserving Model With Claim Openness

Lindholm¹,

Zakrisson²

2021

ASTIN Bull.

View full text Add to dashboard Cite

The present paper introduces a simple aggregated reserving model based on claim count and payment dynamics, which allows for claim closings and re-openings. The modelling starts off from individual Poisson process claim dynamics in discrete time, keeping track of accident year, reporting year and payment delay. This modelling approach is closely related to the one underpinning the so-called double chain-ladder model, and it allows for producing separate reported but not settled and incurred but not reported reserves. Even though the introduction of claim closings and re-openings will produce new types of dependencies, it is possible to use flexible parametrisations in terms of, for example, generalised linear models (GLM) whose parameters can be estimated based on aggregated data using quasi-likelihood theory. Moreover, it is possible to obtain interpretable and explicit moment calculations, as well as having consistency of normalised reserves when the number of contracts tend to infinity. Further, by having access to simple analytic expressions for moments, it is computationally cheap to bootstrap the mean squared error of prediction for reserves. The performance of the model is illustrated using a flexible GLM parametrisation evaluated on non-trivial simulated claims data. This numerical illustration indicates a clear improvement compared with models not taking claim closings and re-openings into account. The results are also seen to be of comparable quality with machine learning models for aggregated data not taking claim openness into account.

show abstract

Section: Data and Notationmentioning

confidence: 99%

Section: Comments On Consistency Of Normalised Reservesmentioning

confidence: 99%

A Collective Reserving Model With Claim Openness

Lindholm¹,

Zakrisson²

2021

ASTIN Bull.

View full text Add to dashboard Cite

show abstract

“…Individual reserving models describe how each claim evolves over time, from the occurrence of the accident until settlement of the claim. In addition to the pioneering works by Arjas (1989) and Norberg (1993Norberg ( , 1999, let us also mention the contributions by Larsen (2007), Zhao et al (2009), Drieskens et al (2012), Rosenlund (2012), Antonio and Plat (2014), Pigeon et al (2013Pigeon et al ( , 2014, and Huang et al (2015Huang et al ( , 2016.…”

Section: Introductionmentioning

confidence: 99%

Collective loss reserving with two types of claims in motor third party liability insurance

Denuit

Trufin

2018

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

This paper adopts the new loss reserving approach proposed by Denuit and Trufin (2016), inspired from the collective model of risk theory. But instead of considering the whole set of claims as a collective, two types of claims are distinguished, those claims with relatively short development patterns and claims requiring longer developments. In each case, the total payment per cell is modelled by means of a Compound Poisson distribution with appropriate assumptions about the severities. A case study based on a motor third party liability insurance portfolio observed over 2004-2014 is used to illustrate the approach proposed in this paper. Comparisons with Chain-Ladder are performed and reveal significant differences in best estimates as well as in Value-at-Risk at high probability levels.

show abstract

“…It appears more convenient and more applicable to practice to statistically model the individual loss reserving with a discrete time framework, similar to Hesselager (1995), Pigeon et al (2013Pigeon et al ( , 2014, and Godecharle and Antonio (2015). Along this line, Huang et al (2015aHuang et al ( , b, 2016) demonstrated a significant reduction in the mean squared error of loss reserves using individual/micro data from the popular aggregate data models that typically employ such methods as the chain-ladder and Bornhuetter-Ferguson. They did this by, respectively, deriving their asymptotic variances and numerically comparing them, thus pointing out a promising direction for more informative loss reserving.…”

Section: Introductionmentioning

confidence: 99%

The Impacts of Individual Information on Loss Reserving

Wang¹,

Wu²,

Qiu³

2020

ASTIN Bull.

Self Cite

View full text Add to dashboard Cite

The projection of outstanding liabilities caused by incurred losses or claims has played a fundamental role in general insurance operations. Loss reserving methods based on individual losses generally perform better than those based on aggregate losses. This study uses a parametric individual information model taking not only individual losses but also individual information such as age, gender, and so on from policies themselves into account. Based on this model, this study proposes a computation procedure for the projection of the outstanding liabilities, discusses the estimation and statistical properties of the unknown parameters, and explores the asymptotic behaviors of the resulting loss reserving as the portfolio size approaching infinity. Most importantly, this study demonstrates the benefits of individual information on loss reserving. Remarkably, the accuracy gained from individual information is much greater than that from considering individual losses. Therefore, it is highly recommended to use individual information in loss reserving in general insurance.

show abstract

Stochastic Loss Reserving in Discrete Time: Individual vs. Aggregate Data Models

Cited by 16 publications

References 20 publications

A Collective Reserving Model With Claim Openness

A Collective Reserving Model With Claim Openness

Collective loss reserving with two types of claims in motor third party liability insurance

The Impacts of Individual Information on Loss Reserving

Contact Info

Product

Resources

About