Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach provides a direct path from unacceptable positions towards the acceptance set. Intrinsic risk measures use only internal resources and return the smallest percentage of the currently held financial position which has to be sold and reinvested into an eligible asset such that the resulting position becomes acceptable. While avoiding the problem of infinite values, intrinsic risk measures allow a free choice of the eligible asset and they preserve desired properties such as monotonicity and quasi-convexity. A dual representation on convex acceptance sets is derived and the link of intrinsic risk measures to their monetary counterparts on cones is detailed.

Risk transfer is a key risk and capital management tool for insurance companies. Transferring risk between insurers is used to mitigate risk and manage capital requirements. We investigate risk transfer in the context of a network environment of insurers and consider capital costs and capital constraints at the level of individual insurance companies. We demonstrate that the optimisation of profitability across the network can be achieved through risk transfer. Considering only individual insurance companies, there is no unique optimal solution and, a priori, it is not clear which solutions are fair. However, from a network perspective, we derive a unique fair solution in the sense of cooperative game theory. Implications for systemic risk are briefly discussed.

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The common risk measure classifies a financial position by the minimal amount of external capital that must be added to the position to make it acceptable.We introduce a new concept: intrinsic risk measures, which provide a more direct path from unacceptable positions towards the acceptance set.