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arXiv · 2207.05982

On the representation of weakly maxitive monetary risk measures and their rate functions

José Miguel Zapata
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Abstract

The present paper provides a representation result for monetary risk measures (i.e., monotone translation invariant functionals) satisfying a weak maxitivity property. This result can be understood as a functional analytic generalization of G\"{a}rtner-Ellis large deviations theorem. In contrast to the classical G\"{a}rtner-Ellis theorem, the rate function is computed on an arbitrary set of continuous real-valued functions rather than the dual space. As an application of the main result, we establish a large deviation result for sequences of sublinear expectations on regular Hausdorff topological spaces.

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José Miguel Zapata. 2022-07-13. On the representation of weakly maxitive monetary risk measures and their rate functions. https://arxiv.org/abs/2207.05982

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