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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert


Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

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2196-7040
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Volume 31, Issue 3-4

Issues

Stochastic dominance with respect to a capacity and risk measures

Miryana Grigorova
Published Online: 2014-11-13 | DOI: https://doi.org/10.1515/strm-2014-1167

Abstract

In our previous work, we have extended the classical notion of increasing convex stochastic dominance relation with respect to a probability to the more general case of a normalized monotone (but not necessarily additive) set function, also called a capacity. In the present paper, we pursue that work by studying the set of monetary risk measures (defined on the space of bounded real-valued measurable functions) satisfying the properties of comonotonic additivity and consistency with respect to the generalized stochastic dominance relation. Under suitable assumptions on the underlying capacity space, we characterize that class of risk measures in terms of Choquet integrals with respect to a distorted capacity whose distortion function is concave. Kusuoka-type characterizations are also established. A generalization to the case of a capacity of the Tail Value at Risk is provided as an example. It is also shown that some well-known results about Choquet integrals with respect to a distorted probability do not necessarily hold true in the more general case of a distorted capacity.

Keywords: Choquet integral; stochastic orderings; quantile function; distortion function; ambiguity; tail value at risk; behavioural finance; Kusuoka's representation; Knightian uncertainty; Choquet risk measure

MSC: 60E15; 91B30; 62P05; 91B06; 28E10

About the article

Received: 2014-04-11

Revised: 2014-09-13

Accepted: 2014-10-29

Published Online: 2014-11-13

Published in Print: 2014-12-01


Citation Information: Statistics & Risk Modeling, Volume 31, Issue 3-4, Pages 259–295, ISSN (Online) 2196-7040, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1515/strm-2014-1167.

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