Risk-minimizing hedging strategies for insurance payment processes

Föllmer and Sondermann (1986) proved the existence of a unique admissible risk-minimizing hedging strategy for any square-integrable contingent claim H in the martingale case. We extend this approach to the situation where the hedger's liabilities are described by a general payment process A and consider some examples related to insurance. These include a general unit-linked life insurance contract driven by a Markov jump process and a claim process from non-life insurance where the claim size distribution is affected by a traded price index.