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

Jérôme Barbarin, Tanguy De Launois and Pierre Devolder

Scandinavian Actuarial Journal, 2009, vol. 2009, issue 2, 119-151

Abstract: 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 Föllmer & Sondermann (1986) and extended by Møller (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.

Date: 2009
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DOI: 10.1080/03461230802281047

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