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 non-life insurance liabilities in hybrid financial and insurance markets, while taking into account the role of inflation under the benchmark approach. This framework offers at the same time a general and flexible structure, and explicit and treatable pricing formula.
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