Stochastic Claims Reserving Methods with State Space Representations: A Review

Often, the claims reserves exceed the available equity of non-life insurance companies and a change in the claims reserves by a small percentage has a large impact on the annual accounts. Therefore, it is of vital importance for any non-life insurer to handle claims reserving appropriately. 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. 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. For this purpose, relevant articles are collected and categorized, and the contents are explained in detail and subjected to a conceptual comparison.

The Negative Impact of COVID-19 on Life Insurers

Understanding COVID-19 induced mortality risk is significant for life insurers to better analyze their financial sustainability after the outbreak of COVID-19. To capture the mortality effect caused by COVID-19 among all ages, this study proposes a temporary adverse mortality jump model to describe the dynamics of mortality in a post-COVID-19 pandemic world based on the weekly death numbers from 2015 to 2021 in the United States. As a comparative study, the Lee-Carter model is used as the base case to represent the dynamics of mortality without COVID-19. Then we compare the force of mortality, the survival probability and the liability of a life insurer by considering COVID-19 and those without COVID-19. We show that a life insurer's financial sustainability will deteriorate because of the higher mortality rates than expected in the wake of COVID-19. Our results remain unchanged when we also consider the effect of interest rate risk by adopting the Vasicek and CIR models.

Developing the Underwriting Process in Life Insurance

Underwriting is the main factor affecting the reliability, stability of the organizational development of the life insurer and determining the quality of financial management, strategic planning, budget management of the life insurer, the economic feasibility of the life insurance process, the adequacy of the life insurer's operational management system. Underwriting is the main business process in insurance organizations and provides for the assessment and management of insurance risk accepted for insurance. This study focuses on the economic nature of underwriting, the approaches of scientists to it, the specifics of life insurance underwriting, types of life insurance underwriting and the process of their implementation, as well as directions and stages of underwriting in life insurance. The article also substantiates that digitalization of the underwriting process in life insurance is an important factor in its development. In concluding life insurance contracts, regardless of the type of insurance product, according to the author, underwriting should be carried out gradually in several directions.

A Bayesian Internal Model for Reserve Risk: An Extension of the Correlated Chain Ladder

The goal of this paper was to exploit the Bayesian approach and MCMC procedures to structure an internal model to quantify the reserve risk of a non-life insurer under Solvency II regulation. To this aim, we provide an extension of the Correlated Chain Ladder (CCL) model to the one-year time horizon. In this way, we obtain the predictive distribution of the next year obligations and we are able to assess a capital requirement compliant with Solvency II framework. Numerical results compare the one-year CCL with other traditional approaches, such as Re-Reserving and the Merz and Wüthrich formula. One-year CCL proves to be a legitimate alternative, providing values comparable with the more traditional approaches and more robust and accurate risk estimations, that embed external knowledge not present in the data and allow for a more precise and tailored representation of the risk profile of the insurer.

The Importance of the Efficiency of Mutual Life Insurers: A Comparison to Stock Life Insurers

Research background: Mutual companies are a major component of the life insurance industry worldwide and moreover are growing in importance. Efficiency, potentially affected by whether a life insurer company is mutual or stock, can determine how well said companies perform.Purpose: The aim of this paper is to demonstrate the importance of examining the efficiency of mutual and takaful (similar to mutuals) life insurance companies.Research methodology: This research coordinates 1) ideas regarding the size and importance of the mutual and takaful life industries worldwide, 2) theoretical aspects concerning how the efficiency of mutual/takafuls is expected to compare to that of stock insurers and 3) the outcomes of germane life insurance efficiency studies.Results: The outcomes of life insurance efficiency studies tend to show that, in total, stock insurers are more efficient than mutuals apart from one conspicuous element. As mutuals are substantial within several of the world’s largest life markets and the global life industry their being inefficient can be exceedingly negative. The overall conclusion is that such inefficiency can lead to dire economic problems so it is imperative to investigate the efficiency of mutuals/takafuls and perhaps the one element of stocks.Novelty: This article is the first to investigate the results of mutual/takaful life insurer efficiency studies in concert with the abovementioned theory and draws a vital conclusion regarding mutual/takaful life insurer inefficiency.

Chain claims reserving methods in non-life insurance

Considering that the reliability of reserves valuation directly influences the financial strength of an insurance company, the main aim of this paper is to present a claims reserving estimation for a Romanian non-life insurer based on the most popular chain methods which are typically used in practice for the estimation of outstanding claims reserves in general insurance industry: Standard Chain Ladder and Munich Chain Ladder both on the claims incurred data and claims paid data. The tail development factors have been estimated based on the curve-fitting methods. The obvious advantage of these methods is represented by its simplicity of the practicality application. The results of the research under two chain claims reserving models reveal significant differences between the Standard Chain Ladder and Munich Chain Ladder with respect to the claims reserves level. Probably the Standard Chain Ladder based on paid method underestimates the outstanding loss liabilities and Standard Chain Ladder based on Incurred method overestimates the claims reserves. The claims reserves predictions under the Paid Munich Chain Ladder and Incurred Munich Chain Ladder are between the two Standard Chain Ladder outstanding loss liabilities estimates. The results of the tail extrapolation shown that the incorporation of the tail factors can have a significant impact on claims predictions.