Browsing by Subject "Laplace principle"

Now showing 1 - 2 of 2
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    Representation of weakly maxitive monetary risk measures and their rate functions
    (Elsevier, 2023-01-31) Zapata García, José Miguel; Estadística e Investigación Operativa
    This article 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 the Gärtner-Ellis large deviations theorem. In contrast to the classical Gärtner-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 deviations result for sequences of sublinear expectations on regular Hausdorff topological spaces.
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    Weakly maxitive set functions and their possibility distributions
    (Elsevier, 2023-03-22) Kupper, Michael; Zapata García, José Miguel; Estadística e Investigación Operativa
    The Shilkret integral with respect to a completely maxitive capacity is fully determined by a possibility distribution. In this paper, we introduce a weaker topological form of maxitivity and show that under this assumption the Shilkret integral is still determined by its possibility distribution for functions that are sufficiently regular. Motivated by large deviations theory, we provide a Laplace principle for maxitive integrals and characterize the possibility distribution under certain separation and convexity assumptions. Moreover, we show a maxitive integral representation result for weakly maxitive non-linear expectations. The theoretical results are illustrated by providing large deviations bounds for sequences of capacities, and by deriving a monotone analogue of Cramér's theorem.