Economy – Quantitative Finance – Risk Management
Scientific paper
2012-03-20
Economy
Quantitative Finance
Risk Management
25 pages
Scientific paper
We consider financial positions belonging to the Banach lattice of bounded measurable functions on a given measurable space. We discuss risk measures generated by general acceptance sets allowing for capital injections to be invested in a pre-specified eligible asset with an everywhere positive payoff. Risk measures play a key role when defining required capital for a financial institution. We address the three critical questions: when is required capital a well-defined number for any financial position? When is required capital a continuous function of the financial position? Can the eligible asset be chosen in such a way that for every financial position the corresponding required capital is lower than if any other asset had been chosen? In contrast to most of the literature our discussion is not limited to convex or coherent acceptance sets and allows for eligible assets that are not necessarily bounded away from zero. This generality uncovers some unexpected phenomena and opens up the field for applications to acceptance sets based both on Value-at-Risk and on Tail Value-at-Risk.
Farkas Walter
Koch-Medina Pablo
Munari Cosimo-Andrea
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