Optimal model points in term life insurance

This thesis is focused on the problem of seeking an optimal set of the model points selection when dealing with a portfolio of term insurance policies and a LIBOR Market Model that determines the dynamics of the forward rates. Specifically, the study is associated to the problem of minimizing a specific risk functional which measures the average discrepancy between two portfolios: the given portfolio of policies and the model points, a small group of representative contracts which substitute the first one, without misrepresenting its inherent risk structure. This optimization process is aimed to reducing the computation difficulties of the valuation of the performance of any portfolios of policies, projections to be made daily by life insurance companies. In particular, in the present thesis, after a brief reference to some basic concepts in the interest rate field, there are described the LIBOR Market Model and the risk functional in a Banach space. The portfolio representation problem is also examined, because it allows to define the dynamics of those portfolios within a certain class that best represents the inherent risk structure of a given financial exposure. Finally, it is analyzed the particular case of the term life insurance.