Risk minimization with inflation and interest rate risk: applications to non-life insurance

This paper aims at studying the asset allocation problem of a non-life insurance company when inflation risk and interest rate risk are taken into account. To this purpose, we apply the risk-minimization theory developed by Follmer Sondermann (1986) and extended by Mller (2001). We derive the general form of the risk-minimizing strategies when the cumulative payments of the insurer are described, as suggested by Arjas (1989), by a process adapted to the natural filtration of a marked point process and when the inflation and the term structure of interest rates are simultaneously described by the HJM model of Jarrow Yildirim (2003). We then apply our general results in two collective models and two individual models of non-life insurance payments