Semiparametric model for prediction of individual claim loss reserving

Zhao, Xiaobing; Zhou, Xian; Wang, Jing Long

doi:10.1016/j.insmatheco.2009.02.009

Cited by 47 publications

(33 citation statements)

References 28 publications

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“…The first approach uses aggregate claim data, which makes it hard to relate person‐specific risk factors to individual claim sizes (Zhao and Zhou, ). The second approach is based on a statistical model that captures the relation between individual claim sizes on the one hand and person‐specific characteristics or other relevant risk factors on the other hand (e.g., Czado and Rudolph, ; Larsen, ; Zhao, Zhou, and Wang ; Antonio and Plat, 2010; Zhao and Zhou, ; Levantesi and Menzietti, ). The statistical model is used to estimate the claim size distribution of a single policyholder with certain risk factors, which provides input for the estimate of an individual liability.…”

Section: Introductionmentioning

confidence: 99%

Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

Spierdijk¹,

Koning²

2013

J of Risk & Insurance

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This article proposes a new method for estimating claim liabilities. Our approach is based on the observation from contract theory that there is information asymmetry between the insurer and the policyholder about the risks incurred by the latter. We show that unobserved heterogeneity allows for a form of experience learning that can reduce this asymmetry, which makes it easier for the insurer to distinguish between high‐risk and low‐risk claimants. We evaluate our approach in the context of disability insurance for self‐employed and show that it results in more accurate best estimates of outstanding claim liabilities.

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Section: Introductionmentioning

confidence: 99%

Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

Spierdijk¹,

Koning²

2013

J of Risk & Insurance

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“…Recently, Larsen (2007) revisited the work of Norberg, Haastrup and Arjas with a small case-study. Zhao et al (2009) and Zhao and Zhou (2010) present a model for individual claims development using (semi-parametric) techniques from survival analysis and copula methods. However, a case study is lacking in their work.…”

Section: Introductionmentioning

confidence: 99%

Micro-Level Stochastic Loss Reserving

Antonio

Plat

2010

SSRN Journal

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Abstract1 To meet future liabilities general insurance companies will set-up reserves. Predicting future cash-flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general insurance business has been developed. Apart from few exceptions, all of these papers are based on data aggregated in run-off triangles. However, such an aggregate data set is a summary of an underlying, much more detailed data base that is available to the insurance company. We refer to this data set at individual claim level as 'micro-level data'. We investigate whether the use of such micro-level claim data can improve the reserving process. A realistic micro-level data set on liability claims (material and injury) from a European insurance company is modeled. Stochastic processes are specified for the various aspects involved in the development of a claim: the time of occurrence, the delay between occurrence and the time of reporting to the company, the occurrence of payments and their size and the final settlement of the claim. These processes are calibrated to the historical individual data of the portfolio and used for the projection of future claims. Through an outof-sample prediction exercise we show that the micro-level approach provides the actuary with detailed and valuable reserve calculations. A comparison with results from traditional actuarial reserving techniques is included. For our case-study reserve calculations based on the micro-level model are to be preferred; compared to traditional methods, they reflect real outcomes in a more realistic way.

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“…(c) Generally, one can base the assumption of claims intensity on her/his a priori knowledge on the claims occurrence process; the more knowledge, the less unknown components of the model. While the model above assumes homogeneous claims intensity, which has been investigated by, e.g., Norberg (1986), Pigeon et al (2013Pigeon et al ( , 2014, another possible model is heterogeneous claims intensity, such as discussed by, e.g., Norberg (1993Norberg ( , 1999, Zhao et al (2009), and Zhao and Zhou (2010). Though what we are discussing is the mathematically simplest homogeneous intensity, an analysis for heterogeneous intensity can be obtained in a similar way due to the adopted discrete-time setting.…”

Section: Model Formulationmentioning

confidence: 91%

“…Larsen (2007) estimated stochastic reserving by means of the decomposition of a PDMPP into independent sections so as to accordingly split likelihood into products that can be maximized separately in isolation. Zhao et al (2009) and Zhao and Zhou (2010) extended the results by allowing dependence between delays and heterogeneous response variable and can contain various covariate effects. More recently, following the framework of Norberg (1993Norberg ( , 1999, Antonio and Plat (2014) analyzed a set of real insurance data from a European company.…”

Section: Introductionmentioning

confidence: 92%

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

Huang

Qiu

2015

Communications in Statistics - Theory and Methods

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In this paper, a stochastic individual data model is considered. It accommodates occurrence times, reporting, and settlement delays and severity of every individual claims. This formulation gives rise to a model for the corresponding aggregate data under which classical chain ladder and Bornhuetter-Ferguson algorithms apply. A claims reserving algorithm is developed under this individual data model and comparisons of its performance with chain ladder and Bornhuetter-Ferguson algorithms are madeto reveal the effects of using individual data to instead aggregate data. The research findings indicate a remarkable promotion in accuracy of loss reserving, especially when the claims amounts are not too heavy-tailed.

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Semiparametric model for prediction of individual claim loss reserving

Cited by 47 publications

References 28 publications

Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

Micro-Level Stochastic Loss Reserving

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

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