In the thesis we first introduce Lévy processes and some important results in the field. Next we present a part of the stochastic analysis for Lévy processes which is important for the pricing of financial derivatives and give special emphasis to the Itô formula for Lévy processes. We continue with the description of some financial derivatives and insurance products. In the continuation we give a method for solving the differential equations and methods of numerical approximation and integration. Finally, we apply these methods and theoretical results to the pricing of financial derivatives, economic scenario generators and pricing variable annuities, especially the product GMWB. Our introduced approach for the latter seems to be new.
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