Some remarks on capital requirement using robust statistics

Author (s)	P. Barrieu and C. Ravanelli
Further Information	Publications and Research Papers\| (P.Barrieu staff page)
Abstract	In a theoretical framework, we investigate capital requirements based on Value at Risk and Average Value at Risk criteria when the true data generating process of the portfolio return is unknown. We provide an approximation formula for such capital requirements where the leading term is based on a feasible estimate of the data generating process. This formula uses a first order Taylor expansion of the Value at Risk and Average Value at Risk around the defiance model parameter of the agent. Errors bounds on such risk measures are obtained. They can be interpreted as the impact of model uncertainty on both the Value at Risk and Average Value at Risk measures.

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Department of Statistics, Columbia House

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