Stochastic chain-ladder reserving with modeled general inflation

We consider two possible approaches to the problem of incorporating explicit general (i.e., economic) inflation in the non-life claims reserve estimates and the corresponding reserve SCR, defined - as in Solvency II - under the one-year view. What we call the actuarial approach provides a simplified solution to the problem, obtained under the assumption of deterministic interest rates and absence of inflation risk premia. The market approach seeks to eliminate these shortcomings by combining a stochastic claims reserving model with a stochastic market model for nominal and real interest rates. The problem is studied in details referring to the stochastic chain-ladder provided by the Over-dispersed Poisson model. The application of the two approaches is illustrated by a worked example based on market data.