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Statistical Theory and Related Fields Volume 6, 2022 - Issue 2
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Articles

Stochastic loss reserving using individual information model with over-dispersed Poisson

Zhigao WangSchool of Statistics, East China Normal University, Shanghai, People's Republic of ChinaCorrespondence[email protected]
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Xianyi WuSchool of Statistics, East China Normal University, Shanghai, People's Republic of ChinaView further author information
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Chunjuan QiuSchool of Statistics, East China Normal University, Shanghai, People's Republic of ChinaView further author information
Pages 114-128 | Received 20 Aug 2020, Accepted 01 Mar 2021, Published online: 19 Mar 2021

Figures & data

Figure 1. The simulated Mr over varying coefficients of covariates. (a) Example 5.1 and (b) Example 5.2.

Figure 1. The simulated Mr over varying coefficients of covariates. (a) Example 5.1 and (b) Example 5.2.

Table 1. The individual information in real data analysis.

Figure 2. Histograms of reporting delays (in days): (a) Female, Region III, age 9–20; (b) Male, Region I, age 45–50; (c) Male, Region VI, age 20–40; (d) Male, Region III, age >55.

Figure 2. Histograms of reporting delays (in days): (a) Female, Region III, age 9–20; (b) Male, Region I, age 45–50; (c) Male, Region VI, age 20–40; (d) Male, Region III, age >55.

Figure 3. Histograms of settlement delays (in days): (a) Female, Region III, age 9–20; (b) Male, Region I, age 45–50; (c) Male, Region VI, age 20–40; (d) Male, Region III, age >55.

Figure 3. Histograms of settlement delays (in days): (a) Female, Region III, age 9–20; (b) Male, Region I, age 45–50; (c) Male, Region VI, age 20–40; (d) Male, Region III, age >55.

Table 2. Estimated parameters for reporting developments, their standard errors and p-values.

Table 3. Estimated parameters for settlements developments, their standard errors and p-values.

Table 4. Estimated parameters γˆ for payments, their standard errors and p-values.

Table 5. Reserving, accuracy of prediction and accuracy improvement of IIM with respect to IDM.

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