Displaying similar documents to “Robustness regions for measures of risk aggregation”

Uncertainty orders on the sublinear expectation space

Dejian Tian, Long Jiang (2016)

Open Mathematics

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In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation 𝔼 has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use...

Quantile hedging on markets with proportional transaction costs

Michał Baran (2003)

Applicationes Mathematicae

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The problem of risk measures in a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk are introduced. This gives a generalization of quantile hedging presented in [4].

Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Pierre Devolder, Adrien Lebègue (2016)

Dependence Modeling

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The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products. Secondly, for such products,we challenge the definition of the Solvency Capital Requirement (SCR) under the Solvency II (SII) regulatory framework based on a yearly viewpoint. Several methods for the calculation of the solvency capital are presented. We start our study with...

Seven Proofs for the Subadditivity of Expected Shortfall

Paul Embrechts, Ruodu Wang (2015)

Dependence Modeling

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Subadditivity is the key property which distinguishes the popular risk measures Value-at-Risk and Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature and some not. One of the main objectives of this paper is to provide a general guideline for instructors to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each proof.With different proofs, different important properties...

Narrow Convergence in Spaces of Set-Valued Measures

Kenny Koffi Siggini (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove an analogue of Topsøe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space.

Thin-shell concentration for convex measures

Matthieu Fradelizi, Olivier Guédon, Alain Pajor (2014)

Studia Mathematica

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We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.

Generalized duration measures in a risk immunization setting. Implementation of the Heath-Jarrow-Morton model

Alina Kondratiuk-Janyska, Marek Kałuszka (2006)

Applicationes Mathematicae

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The aim of this paper is to set different lower bounds on the change of the expected net cash flow value at time H > 0 in general term structure models, referring to the studies of Fong and Vasiček (1984), Nawalkha and Chambers (1996), and Balbás and Ibáñez (1998) among others. New immunization strategies are derived with new risk measures: generalized duration and generalized M-absolute of Nawalkha and Chambers, and exponential risk measure. Furthermore, examples of specific one-factor...