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Life insurance companies rely on mortality rate models to set appropriate premiums for their services. Over the past century, average life expectancy has increased and continues to do so, necessitating more accurate models. Two commonly used models are the Gompertz-Makeham law of mortality and the Lee-Carter model. The Gompertz-Makeham model depends solely on an age variable, while the Lee-Carter model incorporates a time-varying aspect which accounts for the increase in life expectancy over time. This paper constructs both models using training data acquired from Skandia Mutual Life Insurance Company and compares them to validation data from the same set. The study suggests that the Lee-Carter model may be able to offer some improvements compared to the Gompertz-Makeham law of mortality in terms of predicting future mortality rates. However, due to a lack of qualitative data, creating a competitive Lee-Carter model through Singular Value Decomposition, SVD, proved to be problematic. Switching from the current Gompertz-Makeham model to the Lee-Carter model should, therefore, be explored further when more high quality data becomes available.

Life insurance companies rely on mortality rate models to set appropriate premiums for their services. Over the past century, average life expectancy has increased and continues to do so, necessitating more accurate models. Two commonly used models are the Gompertz-Makeham law of mortality and the Lee-Carter model. The Gompertz-Makeham model depends solely on an age variable, while the Lee-Carter model incorporates a time-varying aspect which accounts for the increase in life expectancy over time. This paper constructs both models using training data acquired from Skandia Mutual Life Insurance Company and compares them to validation data from the same set. The study suggests that the Lee-Carter model may be able to offer some improvements compared to the Gompertz-Makeham law of mortality in terms of predicting future mortality rates. However, due to a lack of qualitative data, creating a competitive Lee-Carter model through Singular Value Decomposition, SVD, proved to be problematic. Switching from the current Gompertz-Makeham model to the Lee-Carter model should, therefore, be explored further when more high quality data becomes available.

The study of mortality is an ever-active field of research, and new methods or combinations of methods are constantly being developed. In the actuarial domain, the study of phenomena disrupting mortality and leading to excess mortality, as in the case of COVID-19, is of great interest. Therefore, it is relevant to investigate the extent to which an epidemiological model can be integrated into an actuarial approach in the context of mortality. The aim of this project is to establish a method for the study of excess mortality due to an epidemic and to quantify these effects in the context of the insurance world to anticipate certain possible financial instabilities. We consider a case study caused by SARS-CoV-2 in Belgium during the year 2020. We propose an approach that develops an epidemiological model simulating excess mortality, and we incorporate this model into a classical approach to pricing life insurance products., SCOPUS: ar.j, info:eu-repo/semantics/published

In this thesis, we first go through classical results from the field of credibility theory. One of the most well-known models in the field is the Büuhlmann-Straub model. The model is relatively straightforward to apply in practice and is widely used. A major advantage of the model is its simplicity and intuitive dependency on its model parameters. From our perspective, the main drawback is the assumption regarding uncorrelated data. We show that the correlation can be used to cancel observational noise and therefore obtain more accurate estimators. This leads to an extended credibility formula that contains the Bühlmann-Straub model as a special case. This comes at the cost of introducing singularities which may cause the estimator to behave unexpectedly under certain circumstances. Further research is needed to better understand how often the circumstances are met in practice and if transforming the optimal weights could be a way forward in such cases. Finally, a simulation study based on real-world data shows that the proposed model outperforms the Bühlmann-Straub model.

In this thesis, we first go through classical results from the field of credibility theory. One of the most well-known models in the field is the Büuhlmann-Straub model. The model is relatively straightforward to apply in practice and is widely used. A major advantage of the model is its simplicity and intuitive dependency on its model parameters. From our perspective, the main drawback is the assumption regarding uncorrelated data. We show that the correlation can be used to cancel observational noise and therefore obtain more accurate estimators. This leads to an extended credibility formula that contains the Bühlmann-Straub model as a special case. This comes at the cost of introducing singularities which may cause the estimator to behave unexpectedly under certain circumstances. Further research is needed to better understand how often the circumstances are met in practice and if transforming the optimal weights could be a way forward in such cases. Finally, a simulation study based on real-world data shows that the proposed model outperforms the Bühlmann-Straub model.