Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving

Abstract

In stochastic claims reserving, state space models have been used for almost 40 years to forecast loss reserves and to compute their mean squared error of prediction. Although state space models and the associated Kalman filter learning algorithms are very powerful and flexible tools, comparatively few articles on this topic were published during this period. Most recently, several articles have been published which highlight the benefits of state space models in stochastic claims reserving and may lead to a significant increase in its popularity for applications in actuarial practice. To further emphasize the merits of these papers, this commentary highlights various additional aspects that are useful for practical applications and offer some fruitful directions for future research.

Stochastic Claims Reserving Methods with State Space Representations: A Review

“…As for promising directions for future research in the field of stochastic claims reserving based on state space models, we mainly suggest to conduct micro-level claims reserving and to implement non-linear systems (see Chukhrova and Johannssen (2021)). Moreover, using state space models and beyond, we would like to emphasize the use of granular models as well as of machine learning and soft computing techniques in future research projects.…”

“…Therefore, appropriate claims reserves for the outstanding loss liabilities have to be calculated by the responsible actuary. Since these loss reserves are often the largest share on the liability side of the balance sheet, adequate claims reserving is required, that is, forecasting these liabilities and quantifying their uncertainty is a key actuarial issue (see Chukhrova and Johannssen 2021).…”

“…Although claims data are time series data, the majority of the proposed (stochastic) claims reserving methods is not based on time series models. Among the time series models, state space models combined with Kalman filter learning algorithms have proven to be very advantageous as they provide high flexibility in modeling and an accurate detection of the temporal dynamics of a system (see Chukhrova and Johannssen 2021). Against this backdrop, this paper aims to provide a comprehensive review of stochastic claims reserving methods that have been developed and analyzed in the context of state space representations.…”

“…Depending on the modeling (e.g., via a Hoerl curve or the log-normal model), these additional observations induce correspondingly increasing state vectors, system matrices, hyper-parameters and noise terms. This can complicate parameter estimation, practical handling, and simultaneous involvement of multiple run-off triangles considerably (see Chukhrova and Johannssen 2021).…”

Model Error (or Ambiguity) and Its Estimation, with Particular Application to Loss Reserving

“…For example, the sensitivity of forecasts to individual observations within a claim array has been investigated by Avanzi et al (2023). Chukhrova and Johannssen (2021) follow up De Jong and Zehnwirth (1983), mentioned above, in examining state space models for…”