Models of Capital Requirements in Static and Dynamic Settings

The aim of this paper is twofold. First, we generalize the notion of capital requirement, originally formulated in a regulatory framework, in order to unify other apparently diverse financial concepts. Second, we stress the interpretation of a capital requirement as a measure of risk, providing a link with the theory of coherent risk measures. We define a capital requirement as the minimal initial cost of a hedging action that makes the original position acceptable. Three basic elements are involved in such a methodology: a system of prices, a class of permitted hedging actions and a criterion of acceptability. Our approach is very general, because we construct capital requirements on vector spaces. However, we will give some concrete applications related, in particular, to the availability of a financial market, to the presence of different business units in an institution or to the fact that pay-offs are spread over different dates.

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