“…The insurer is enforced hold risk capital given by ρĝ I (X − f (X), P I ) − E P I [X − f (X)], where ρĝ I (X − f (X), P I ),ĝ I ∈ G, is a distortion risk measure used to determine the risk capital is based on the probability measure P I . Such a valuation principle is used commonly in practice and is embedded in regulatory requirements under the Swiss Solvency Test and Solvency II (see, e.g., Chi [25], Asimit et al [26], and Cheung and Lo [15]). The wealth at a pre-determined future time for the insurer is given bŷ…”