Stochastic orderings with respect to a capacity and an application to a financial optimization problem

Grigorova Miryana ()
Additional contact information
Grigorova Miryana: Laboratoire de Probabilités et Modèles Aléatoires (CNRS-UMR 7599); Université Paris Diderot (Paris 7); 5 rue Thomas Mann; 75013 Paris; France

Statistics & Risk Modeling, 2014, vol. 31, issue 2, 183-213

Abstract: By analogy with the classical case of a probability measure, we extend the notion of increasing convex (concave) stochastic dominance relation to the case of a normalized monotone (but not necessarily additive) set function also called a capacity. We give different characterizations of this relation establishing a link to the notions of distribution function and quantile function with respect to the given capacity. The Choquet integral is extensively used as a tool. In the second part of the paper, we give an application to a financial optimization problem whose constraints are expressed by means of the increasing convex stochastic dominance relation with respect to a capacity. The problem is solved by using, among other tools, a result established in our previous work, namely a new version of the classical upper (resp. lower) Hardy–Littlewood's inequality generalized to the case of a continuous from below concave (resp. convex) capacity. The value function of the optimization problem is interpreted in terms of risk measures (or premium principles).

Keywords: Stochastic orderings; increasing convex stochastic dominance; Choquet integral; quantile function with respect to a capacity; stop-loss ordering; Choquet expected utility; distorted capacity; generalized Hardy–Littlewood's inequalities; distortion risk measure; premium principle; ambiguity; non-additive probability; Stochastic orderings; increasing convex stochastic dominance; Choquet integral; quantile function with respect to a capacity; stop-loss ordering; Choquet expected utility; distorted capacity; generalized Hardy–Littlewood's inequalities; distortion risk measure; premium principle; ambiguity; non-additive probability (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/strm-2013-1151 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:31:y:2014:i:2:p:31:n:4

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1515/strm-2013-1151

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().