Processing math: 80%
Miljkovic, Tatjana. 2025. “Premium Estimation Under Model Uncertainty: Model Averaging for Left-Truncated Reinsurance Losses.” Variance 18 (July).
Download all (6)
  • Figure 1. Histogram of Secura Re reinsurance losses with the dashed vertical lines representing eight selected retention levels r{3.0,3.5,4.0,4.5,5.0,5.5,6.0,7.0}r{3.0,3.5,4.0,4.5,5.0,5.5,6.0,7.0}.
  • Figure 2. Panel plot illustrates the summary of relative errors for c=1.2c=1.2. The plot is organized in four rows, each representing a combination of sample size and model space. The first row corresponds to a sample size of n=500n=500 with M1M1, the second row to n=1,000n=1,000 with M1M1, the third row to n=500n=500 with M2M2, and the fourth row to n=1,000n=1,000 with M2M2. Each row contains box plots for four methods: MA-BIC (soft lavender), MA-AIC (light coral), BEST-BIC (pale green), and BEST-AIC (pale blue).
  • Figure 3. Panel plot illustrates the summary of relative errors for c=0.8c=0.8. The plot is organized in four rows, each representing a combination of sample size and model space. The first row corresponds to a sample size of n=500n=500 with M1M1, the second row to n=1,000n=1,000 with M1M1, the third row to n=500n=500 with M2M2, and the fourth row to n=1,000n=1,000 with M2M2. Each row contains box plots for four methods: MA-BIC (soft lavender), MA-AIC (light coral), BEST-BIC (pale green), and BEST-AIC (pale blue).
  • Figure 4. Line plots of ¯RE organized for all combinations of the simulation settings as follows: sample size (in columns): 500, 1,000; method of estimation: BEST-AIC (solid), MA-AIC (dotted), BEST-BIC (dashed), and MA-BIC (dotdashed); truncation point denoted as C08 and C12 for 0.8 and 1.2, respectively (across two rows); two scenarios labeled as “in” corresponding to M1 and “out” corresponding to M2 (by row).
  • Figure 5. Line plots show the standard deviation of RE values organised for all combinations of the simulation settings as follows: sample size (in columns): 500, 1,000; method of estimation: BESTAIC (solid), MA-AIC (dotted), BEST-BIC (dashed), and MA-BIC (dotdashed); truncation point denoted as C08 and C12 for 0.8 and 1.2, respectively (across two rows); two scenarios labeled as “in” corresponding to M1 and “out” corresponding to M2 (by row).
  • Figure 6. Panel plot illustrates the summary of relative errors for c=1.2c=1.2. The plot is organized in two rows, each representing a combination of sample size and model space. The first row corresponds to a sample size of n=50n=50 with M1M1, the second row corresponds to a sample size n=50n=50 with M2M2. Each row contains box plots for four methods: MA-BIC (soft lavender), MA-AIC (light coral), BEST-BIC (pale green), and BEST-AIC (pale blue).

Abstract

In this paper, model averaging (MA) is proposed as a technique to address model uncertainty when estimating the premium for aggregate excess of loss reinsurance. Despite its intrinsic appeal, the use of MA in premium calculations involving left-truncated reinsurance losses remains largely unexplored. In this study, we examine the effectiveness of MA in estimating excess of loss premiums using both real-world data and Monte Carlo simulations. A model space of finite mixtures based on lognormal and gamma distributions is considered for fitting the left-truncated reinsurance losses. Premium estimates are computed based on all models in the considered model space. For a given retention level, closed-form solutions have been derived for the MA premium estimators based on gamma and lognormal mixtures. We examine how well MA estimators perform in comparison to estimators derived from the best model within a given model space, determined by criteria like the Akaike information criterion and Bayesian information criterion. This investigation offers an alternative approach for actuaries and risk managers to estimate premiums while taking model uncertainty into account.

Accepted: May 25, 2025 EDT