Due to regulation reasons, life insurance undertakings have long been struggling with interest rate variations. In the post-ﬁnancial-crisis era, most life insurance ﬁrms in Western countries are facing two major challenges, the one is the dropdown of interest rates and the other is the increase of longevity. Many supervisory authorities have warned life insurance undertakings in their countries that their current portfolios are not adaquate to generate enough returns for future payments to the insured, because most of their assets are made of ﬁxed-income products. The consequence of low interest rates and increasing longevity is that premiums are becoming more expensive and the company s technical provisions are becoming higher than before, which will reduce life insurance undertakings competitive conditions compared to other ﬁnancial institutions. The varying nature and crucial importance of interest rates make it unrealistic to assume them as constant in calculating prospective reserves, especially when it is taken into account the fact that most life insurance products last decades long or even life-long. This thesis explores the possibility of calculating prospective reserves when interest rates are assumed varying. Since stochastic interest rates are represented in bond markets, a unit-linked scheme will be utilized to connect the insurance market to the bond market. A more realistic assumption than varying interest rates is varying interest rates with jumps. L´evy processes are a good candidate for modelling stochastic interest rates with jumps, and hence will be applied in this thesis. However, the permission of jumps in the pricing model will destroy the market-completeness assumption, making it necessary to use a speciﬁc criterion for selecting a risk-neutral probability measure for discounting future cash ﬂows. In this thesis, an Esscher transform will be applied since it preserves the L´evy process. The result of the recursive formula for calculating prospective reserves with stochastic interest rates with jumps is an integro-partial diﬀerential equation which in general does not have an analytical solution.