Abstract
Financial institutions aim to cap the market risk taken by their trading divisions through limited providing of risk capital or setting risk limits, respectively. Risk limits must be based on the market risk model internally used. The paper addresses to the questions of how to efficiently allocate risk capital and how to consistently construct hierarchical systems of risk limits. We develop a very concrete model to allocate risk capital and to control market risk in trading divisions of financial institutions. Based on Value-at-Risk we show how to build up a consistent system of risk limits which guarantees both an optimal profitability and limiting market risk. An optimization approach is used to construct a system of risk limits for any hierarchical order of trading portfolios. Because of instable or simply unknown correlations between portfolio's loss variables there is in result a trade-off between exploiting risk capital and strictly keeping to risk limits.
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