Abstract

Numerous methods have been proposed throughout the literature for decomposing liabilities into risk factors. Such analysis is of great importance because it allows for explaining the impact of each source of risk in relation to the total risk, and thus it allows actuaries to have a certain degree of control over uncertainties. In an insurance context, such sources usually consist of the mortality risk, represented in this paper by the systematic and by the unsystematic mortality risk, and of the investment risk. The objective of this thesis is to consider the Martingale Representation Theorem (MRT) introduced by Schilling et al., (2015) for such risk decomposition, because this method allows for a detailed analysis of the influence of each source of risk. The proposed dynamic models used in this thesis are the Lee-Carter model for the mortality rates and, the arbitrage-free Nelson-Siegel (AFNS) models for the interest rates. These models are necessary in providing accuracy by improving the overall predictive performance. Once, the risk decomposition has been achieved, quantifying the relative importance of each risk factor under different risk measurements is then proceeded. The numerical results are based on annuities and insurances portfolios. It is found that for extended coverage periods, investment risk represents most of the risk while for shorter terms, the unsystematic mortality risk takes larger importance. It is also found that the systematic mortality risk is almost negligible.