The One-Year Runoff Uncertainty for Discounted Claims Reserves

In old accounting tradition, non-life insurance companies have estimated nominal claims reserves for their outstanding loss liabilities. The new Solvency II developments require from non-life insurance companies that they go over to a market-consistent valuation of their insurance liabilities (full balance sheet approach) and that they prove solvency on a yearly basis. As a consequence non-life insurance companies need to consider discounted claims reserves and they need to yearly adjust these claims reserves for the outstanding loss liabilities according to the latest information available. In the present paper we study this one-year adjustment (one-year claims development result) for discounted claims reserves in a stochastic framework: For the purely insurance technical side the Bayes chain ladder model is used, the interest rate risk is described by an appropriate covariance matrix obtained from the Vasicek model.