arXiv subjects

Anas Abdallah

Publications and source records attributed to Anas Abdallah.

3 recordsLinked to original sources

arXiv2025

A Unified Micro-Model for Loss Reserves, IBNR and Unearned Premium Risk with Dependence, Inflation, and Discounting

This paper introduces a unified micro-level stochastic framework for the joint modeling of loss reserves (RBNS), incurred but not reported (IBNR) reserves, and unearned premium risk under dependence, inflation, and discounting. The proposed framework accommodates interactions between indemnities, expenses, reporting delays, and settlement delays, while allowing for flexible parametric dependence structures and dynamic financial adjustments. An Aggregate Trend Renewal Process (ATRP) is used as one possible implementation of the joint model for payments, expenses, and delays; however, the methodological contribution of the paper lies in the unified micro-level reserving architecture rather than in the ATRP itself. The framework produces forward-looking reserve and premium risk measures with direct applications to pricing, reserving, and capital management. We implement the framework using an aggregate trend renewal process at the individual claim level, which can be applied to the usual run-off triangle to obtain predictions for each accident-development year. Closed-form expressions for the first two raw and joint conditional moments of predicted payments are derived, together with approximations of their distribution functions. A detailed case study on medical malpractice insurance illustrates the practical relevance of the approach and its calibration on real-world data. We also investigate data heterogeneity, parameter uncertainty, distributional approximations, premium risk, UPR sensitivity to operational delays and inflation, and risk capital implications under alternative assumptions. The results highlight the advantages of unified micro-level modeling for dynamic liability and premium risk assessment in long-tailed lines of business.

stat.AP↗

arXiv2025

Penalized Copula Mixed Models for Intercompany Loss Reserving and Risk Capital

Intercompany loss reserving provides an opportunity to improve reserve estimation by borrowing information across insurers while accounting for company-level heterogeneity. We propose a penalized generalized copula mixed model for multivariate loss reserving and risk capital analysis using multiple companies' loss triangles. The framework combines mixed-effects marginal models with company-specific copula dependence parameters, allowing residual dependence between lines of business to vary across insurers. Penalization is introduced through an $L_1$ penalty on the fixed effects to stabilize estimation in the tail of the loss triangles, where observations are limited. Estimation is carried out using an iterative two-stage procedure that combines likelihood-based estimation of the marginal mixed models with rank-based copula estimation using residual pseudo-observations. To obtain predictive reserve distributions, we develop a modified bootstrap procedure that accommodates penalized estimation while preserving the dependence structure. Using Schedule P data from the National Association of Insurance Commissioners, we show that the proposed model provides a more stable decomposition of unpaid losses across lines of business, reduces predictive variability relative to silo and fixed-effect copula benchmarks, and leads to lower risk capital after accounting for diversification. A simulation study further evaluates parameter recovery, sparsity selection, reserve accuracy, and robustness to random-effect misspecification. Overall, the proposed model offers an interpretable and flexible framework for intercompany multivariate reserving and capital assessment.

stat.ME↗

arXiv2024

Recurrent Neural Networks for Multivariate Loss Reserving and Risk Capital Analysis

In the property and casualty (P&C) insurance industry, reserves comprise most of a company's liabilities. These reserves are the best estimates made by actuaries for future unpaid claims. Notably, reserves for different lines of business (LOBs) are related due to dependent events or claims. While the actuarial industry has developed both parametric and non-parametric methods for loss reserving, only a few tools have been developed to capture dependence between loss reserves. This paper introduces the use of the Deep Triangle (DT), a recurrent neural network, for multivariate loss reserving, incorporating an asymmetric loss function to combine incremental paid losses of multiple LOBs. The input and output to the DT are the vectors of sequences of incremental paid losses that account for the pairwise and time dependence between and within LOBs. In addition, we extend generative adversarial networks (GANs) by transforming the two loss triangles into a tabular format and generating synthetic loss triangles to obtain the predictive distribution for reserves. We call the combination of DT for multivariate loss reserving and GAN for risk capital analysis the extended Deep Triangle (EDT). To illustrate EDT, we apply and calibrate these methods using data from multiple companies from the National Association of Insurance Commissioners database. For validation, we compare EDT to the copula regression models and find that the EDT outperforms the copula regression models in predicting total loss reserve. Furthermore, with the obtained predictive distribution for reserves, we show that risk capitals calculated from EDT are smaller than that of the copula regression models, suggesting a more considerable diversification benefit. Finally, these findings are also confirmed in a simulation study.

stat.AP↗