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6 results for surplus-invariant

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the fact that acceptability …

2014-01-14abs ↗pdf ↗

A new capital adequacy test is proposed based on value-at-risk.

problem Regulator's need for a capital adequacy test that doesn't depend on firms' surplus or currency.
method Proving that the only surplus-invariant, law-invariant, and conic acceptance set is the set of positions with negative value-at-risk.
result The value-at-risk test is the only possible capital adequacy test under specified conditions.

This paper reviews incompatibilities of comonotonic risk measures.

problem Incompatibilities of comonotonic risk measures with central properties.
method Literature review and Choquet representation of comonotonic additive risk measures.
result Comonotonic additive risk measures cannot be surplus invariant.

The strong Fatou property is crucial for risk measures' dual representations.

problem Ensuring nice dual representations of risk measures.
method Exploring Fatou-type properties and inf-convolutions of law-invariant or surplus-invariant risk measures.
result Every quasiconvex law-invariant functional on a rearrangement invariant space with the strong Fatou property is σ(X, L∞)-lower semicontinuous.