Hedging life insurance contracts in a Lévy process financial market

Starting from the model of Møller [Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin 28 (1998) 17–47] we derive analogously, but for an incomplete financial market, a (locally) risk-minimizing hedging strategy for unit-linked life insurance contracts represented by the pure endowment and the term insurance. The incomplete financial market is exemplarily given by a general Lévy-driven model. We investigate the Föllmer–Schweizer decomposition of their intrinsic value. Additionally, we compare our results to the ones obtained by Møller [Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin 28 (1998) 17–47] and show how they are affected by replacing the complete financial market by an incomplete one.