What is an acceptance set?

An acceptance set is usually associated with risk measures in the world of financial mathematics. The term describes the proposal of a future net worth of a company or a security that is deemed as acceptable by the organisation or body that is regulating said company or market.

Where have you heard about acceptance sets?

If you’re familiar with risk measures, or have employed the use of detailed mathematical analysis when looking to make financial decisions – for example whether or not to invest in a company – you may be aware of acceptance sets.

What you need to know about acceptance sets.

As well as relating to risk measures, acceptance sets can also be associated with superhedging prices. In this case, the acceptance set is seen as the negative of the set of values of a self-financing portfolio at the terminal time. In their paper ‘Measures of Systemic Risk’, Zachary Feinstein, Birgit Rudloff and Stefan Weber mention acceptance sets, stating that for any risk measure, the family of positions with non-positive risk is the acceptance set of the risk measure. The risk measurement of any position can be recovered as a capital requirement, meaning that the axiomatic theory of risk measures could be based on acceptance sets instead of risk measures.