Cost-of-Capital Margin for a General Insurance Liability Runoff

Under new solvency regulations, general insurance companies need to calculate a risk margin to cover possible shortfalls in their liability runoff. A popular approach for the calculation of the risk margin is the so-called cost-of-capital approach. The cost-of-capital approach involves the consideration of multiperiod risk measures. Because multiperiod risk measures are complex mathematical objects, various proxies are used to calculate this risk margin. Of course, the use of proxies and the study of their quality raises many questions, see IAA position paper [7]. In the present paper we derive the first mathematically rigorous multiperiod cost-of-capital approach for a general insurance liability runoff (within a chain ladder framework). We derive analytic formulas for the risk margin which allow to compare the different proxies used in practise. Moreover, a case study investigates and answers questions raised in [7].