Reference : Convex Capital Requirements for Large Portfolios
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Convex Capital Requirements for Large Portfolios
Föllmer, Hans [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Knispel, Thomas []
Stochastic Analysis and Applications to Finance. Essays in Honour of Jia-an Yan
World Scientific Publishing Company
[en] For a large homogeneous portfolio of financial positions, we study the asymptotic behavior of the capital requirement per position defined in terms of a convex monetary risk measure. In an actuarial context, this capital requirement can be seen as a premium per contract. We show that the premia converge to the fair premium as the portfolio becomes large, and we give a precise description of the decay of the risk premia. The analysis is carried out first for a law-invariant convex risk measure and then in a situation of model ambiguity.

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