2. The cost-of-capital margin
In this section we derive the cost-of-capital margin without mathematical details, they are found in Section 3. We consider time periods (years) 1, . . . , T, corresponding time points 0, 1, . . . , T, and a filtered probability space (Ω, F, F, P), where F = (Ft) T t=0 with {∅, Ω} = F0 ⊆ · · · ⊆ FT = F. A liability cash flow corresponds to an F-adapted stochastic process Xo = (Xo t ) T t=1 interpreted as a cash flow from an aggregate insurance liability in runoff. Our aim is to give a precise meaning to the market-consistent value of the liability by taking capital costs into account, and provide results that allow this value to be computed. When the value of an insurance liability cash flow includes capital costs from capital requirements based on future values of both assets and liabilities, the liability value depends on the future values of all assets, including assets held for investment purpose only. In particular, two companies with identical liability cash flows would assign different market-consistent values to the two identical cash flows. This has undesired implications. Instead, as is done in e.g. [11] and prescribed by EIOPA, see [9, Article 38], we take the point of view that an aggregate liability cash flow should be valued by considering a hypothetical transfer of the liability to a separate entity, a socalled reference undertaking, whose assets have the sole purpose of matching the value of the liability as well as possible.
