Incurred chain ladder has implicit inflations in LDFs. For long tail lines, I have only seen a couple of “frequency & severity” based models, where historical claims are indexed to the valuation date first. Historical inflation assumptions are normally derived from CPI and/or average weekly earnings data. Future claims size inflation and superimposed inflation is also applied to future “average claim size” and sometimes to IBNR claim counts. Interest rate only affects the discounted reserve, and normally the risk fee rate is derived from the government bond yields with some sorts of interpolations.