  In this paper we propose a general framework for modeling an insurance
liability cash flow in continuous time, by generalizing the reduced-form
framework for credit risk and life insurance. In particular, we assume a
nontrivial dependence structure between the reference filtration and the
insurance internal filtration. We apply these results for pricing and hedging
non-life insurance liabilities in hybrid financial and insurance markets, while
taking into account the role of inflation under the benchmarked
risk-minimization approach. This framework offers at the same time a general
and flexible structure, and an explicit and treatable pricing-hedging formula.
