Stochastic Non-Life Reserve Estimation and Risk Adjustments under IFRS 17

Date

2025-1-10

Author

Akarsu Şengöz, Gülçin

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Claim reserving is always a critical concept in the insurance sector. Various approaches, both stochastic and deterministic, are developed and extensively discussed in the literature; deterministic approaches, such as the Chain Ladder (CL) model, are preferred by many practitioners because of their straightforward application. It uses the run-off triangle of paid (or incurred) claims and development factors to predict future reserves. However, they might yield a risk of underestimating or overestimating the reserve estimation due to their lack of ability to capture the randomness in the claims amounts, occurrence, and reported time. Therefore, various techniques are developed to overcome or improve these obstacles in deterministic ones. In this thesis, we apply a time-varying Geometric Brownian Motion (GBM) model to annual development factors to estimate ultimate reserves. We propose the Modified Brownian Bridge (BB) as a non-decreasing stochastic process to increase the time interval while maintaining the structure of claim data. By transforming annual data into monthly intervals, this method reduces over-fitting and makes it possible to model claims behavior more precisely. Furthermore, the thesis also incorporates the International Financial Reporting Standards (IFRS 17) risk adjustment (RA) technique into the reserve estimation framework. In the direction of IFRS 17 regulations, a quantile approach is used to calculate the corresponding RA values under the heavy-tailed distributional assumption such as Log-normal, Gamma and Weibull. Unlike most studies in the literature and educational notes in the sector, we utilize the stochastic discount rate, assumed to follow Cox-Ingersol-Ross (CIR) model, to evaluate discounted ultimate reserves required in RA calculation. The Expectation-Maximization (EM) approach is used for parameter estimation in light of the computational difficulties posed by the complex likelihood function of the CIR model. It is supported by the pseudo-log-likelihood technique and normal approximation. The study explores the sensitivity and robustness of both models, GBM and CL, based on the simulations having the recommended risk measures, VaR and TVaR, and percentiles by IRFS 17. The outputs of RA calculation and the behavior of both models to extremely shocked events are presented.

Subject Keywords

Stochastic reserve estimation, Geometric Brownian Motion, Cox-Ingersoll-Rox, Expectation maximization, risk adjustment, IFRS 17

URI

https://hdl.handle.net/11511/113450

Collections

Graduate School of Applied Mathematics, Thesis