Risk excess measures induced by hemi-metrics View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-06-05

AUTHORS

Olivier P. Faugeras, Ludger Rüschendorf

ABSTRACT

The main aim of this paper is to introduce the notion of risk excess measure, to analyze its properties, and to describe some basic construction methods. To compare the risk excess of one distribution Q w.r.t. a given risk distribution P, we apply the concept of hemi-metrics on the space of probability measures. This view of risk comparison has a natural basis in the extension of orderings and hemi-metrics on the underlying space to the level of probability measures. Basic examples of these kind of extensions are induced by mass transportation and by function class induced orderings. Our view towards measuring risk excess adds to the usually considered method to compare risks of Q and P by the values ρ(Q), ρ(P) of a risk measure ρ. We argue that the difference ρ(Q)−ρ(P) neglects relevant aspects of the risk excess which are adequately described by the new notion of risk excess measure. We derive various concrete classes of risk excess measures and discuss corresponding ordering and measure extension properties. More... »

PAGES

6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s41546-018-0032-0

DOI

http://dx.doi.org/10.1186/s41546-018-0032-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1104398298


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/15", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Commerce, Management, Tourism and Services", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1502", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Banking, Finance and Investment", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Toulouse School of Economics - Universit\u00e9 Toulouse 1 Capitole, Manufacture des Tabacs, 21 All\u00e9e de Brienne, 31000, Toulouse, France", 
          "id": "http://www.grid.ac/institutes/grid.22147.32", 
          "name": [
            "Toulouse School of Economics - Universit\u00e9 Toulouse 1 Capitole, Manufacture des Tabacs, 21 All\u00e9e de Brienne, 31000, Toulouse, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Faugeras", 
        "givenName": "Olivier P.", 
        "id": "sg:person.010630315233.97", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010630315233.97"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Abteilung f\u00fcr Mathematische Stochastik, Albert-Ludwigs University of Freiburg, Eckerstrasse 1, D-79104, Freiburg, Germany", 
          "id": "http://www.grid.ac/institutes/grid.5963.9", 
          "name": [
            "Abteilung f\u00fcr Mathematische Stochastik, Albert-Ludwigs University of Freiburg, Eckerstrasse 1, D-79104, Freiburg, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "R\u00fcschendorf", 
        "givenName": "Ludger", 
        "id": "sg:person.012503363065.66", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012503363065.66"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-94-011-3466-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028525555", 
          "https://doi.org/10.1007/978-94-011-3466-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-04790-3_1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006470847", 
          "https://doi.org/10.1007/978-3-662-04790-3_1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00532695", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049811624", 
          "https://doi.org/10.1007/bf00532695"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4419-5821-1_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024571704", 
          "https://doi.org/10.1007/978-1-4419-5821-1_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-33590-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009531412", 
          "https://doi.org/10.1007/978-3-642-33590-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/b12016", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1085139445", 
          "https://doi.org/10.1007/b12016"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00780-004-0127-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044827328", 
          "https://doi.org/10.1007/s00780-004-0127-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-0-387-68276-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004453686", 
          "https://doi.org/10.1007/978-0-387-68276-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00532047", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035215282", 
          "https://doi.org/10.1007/bf00532047"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4614-4869-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026538160", 
          "https://doi.org/10.1007/978-1-4614-4869-3"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-06-05", 
    "datePublishedReg": "2018-06-05", 
    "description": "The main aim of this paper is to introduce the notion of risk excess measure, to analyze its properties, and to describe some basic construction methods. To compare the risk excess of one distribution Q w.r.t. a given risk distribution P, we apply the concept of hemi-metrics on the space of probability measures. This view of risk comparison has a natural basis in the extension of orderings and hemi-metrics on the underlying space to the level of probability measures. Basic examples of these kind of extensions are induced by mass transportation and by function class induced orderings. Our view towards measuring risk excess adds to the usually considered method to compare risks of Q and P by the values \u03c1(Q), \u03c1(P) of a risk measure \u03c1. We argue that the difference \u03c1(Q)\u2212\u03c1(P) neglects relevant aspects of the risk excess which are adequately described by the new notion of risk excess measure. We derive various concrete classes of risk excess measures and discuss corresponding ordering and measure extension properties.", 
    "genre": "article", 
    "id": "sg:pub.10.1186/s41546-018-0032-0", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1290466", 
        "issn": [
          "2095-9672", 
          "2367-0126"
        ], 
        "name": "Probability, Uncertainty and Quantitative Risk", 
        "publisher": "American Institute of Mathematical Sciences (AIMS)", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "3"
      }
    ], 
    "keywords": [
      "probability measure", 
      "excess measures", 
      "distribution P", 
      "kinds of extensions", 
      "basic examples", 
      "measure \u03c1", 
      "extension property", 
      "function classes", 
      "new notion", 
      "concrete classes", 
      "natural basis", 
      "ordering", 
      "space", 
      "class", 
      "extension", 
      "basic construction methods", 
      "mass transportation", 
      "construction method", 
      "properties", 
      "risk comparisons", 
      "notion", 
      "main aim", 
      "kind", 
      "relevant aspects", 
      "measures", 
      "concept", 
      "view", 
      "comparison", 
      "values", 
      "transportation", 
      "basis", 
      "aspects", 
      "excess", 
      "aim", 
      "differences", 
      "levels", 
      "risk excess", 
      "risk", 
      "method", 
      "example", 
      "paper"
    ], 
    "name": "Risk excess measures induced by hemi-metrics", 
    "pagination": "6", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1104398298"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1186/s41546-018-0032-0"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1186/s41546-018-0032-0", 
      "https://app.dimensions.ai/details/publication/pub.1104398298"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-05-20T07:34", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_784.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1186/s41546-018-0032-0"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1186/s41546-018-0032-0'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s41546-018-0032-0'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s41546-018-0032-0'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s41546-018-0032-0'


 

This table displays all metadata directly associated to this object as RDF triples.

149 TRIPLES      22 PREDICATES      76 URIs      58 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1186/s41546-018-0032-0 schema:about anzsrc-for:15
2 anzsrc-for:1502
3 schema:author Naddfc48a0d3c4c5391499d54db853acf
4 schema:citation sg:pub.10.1007/978-0-387-68276-1
5 sg:pub.10.1007/978-1-4419-5821-1_4
6 sg:pub.10.1007/978-1-4614-4869-3
7 sg:pub.10.1007/978-3-642-33590-7
8 sg:pub.10.1007/978-3-662-04790-3_1
9 sg:pub.10.1007/978-94-011-3466-8
10 sg:pub.10.1007/b12016
11 sg:pub.10.1007/bf00532047
12 sg:pub.10.1007/bf00532695
13 sg:pub.10.1007/s00780-004-0127-6
14 schema:datePublished 2018-06-05
15 schema:datePublishedReg 2018-06-05
16 schema:description The main aim of this paper is to introduce the notion of risk excess measure, to analyze its properties, and to describe some basic construction methods. To compare the risk excess of one distribution Q w.r.t. a given risk distribution P, we apply the concept of hemi-metrics on the space of probability measures. This view of risk comparison has a natural basis in the extension of orderings and hemi-metrics on the underlying space to the level of probability measures. Basic examples of these kind of extensions are induced by mass transportation and by function class induced orderings. Our view towards measuring risk excess adds to the usually considered method to compare risks of Q and P by the values ρ(Q), ρ(P) of a risk measure ρ. We argue that the difference ρ(Q)−ρ(P) neglects relevant aspects of the risk excess which are adequately described by the new notion of risk excess measure. We derive various concrete classes of risk excess measures and discuss corresponding ordering and measure extension properties.
17 schema:genre article
18 schema:inLanguage en
19 schema:isAccessibleForFree true
20 schema:isPartOf Nd1e01ea426d849c5b8d679907fbaed82
21 Nd9db7ce09c2249769cbd35a5a16a6a3d
22 sg:journal.1290466
23 schema:keywords aim
24 aspects
25 basic construction methods
26 basic examples
27 basis
28 class
29 comparison
30 concept
31 concrete classes
32 construction method
33 differences
34 distribution P
35 example
36 excess
37 excess measures
38 extension
39 extension property
40 function classes
41 kind
42 kinds of extensions
43 levels
44 main aim
45 mass transportation
46 measure ρ
47 measures
48 method
49 natural basis
50 new notion
51 notion
52 ordering
53 paper
54 probability measure
55 properties
56 relevant aspects
57 risk
58 risk comparisons
59 risk excess
60 space
61 transportation
62 values
63 view
64 schema:name Risk excess measures induced by hemi-metrics
65 schema:pagination 6
66 schema:productId Na2c1116f096648b7ad59651c46c3115b
67 Nd79d37b347344f57a74e0d266cab1d48
68 schema:sameAs https://app.dimensions.ai/details/publication/pub.1104398298
69 https://doi.org/10.1186/s41546-018-0032-0
70 schema:sdDatePublished 2022-05-20T07:34
71 schema:sdLicense https://scigraph.springernature.com/explorer/license/
72 schema:sdPublisher Neae5e119e5cb4c7abe4bcb8cde987a8c
73 schema:url https://doi.org/10.1186/s41546-018-0032-0
74 sgo:license sg:explorer/license/
75 sgo:sdDataset articles
76 rdf:type schema:ScholarlyArticle
77 Na2c1116f096648b7ad59651c46c3115b schema:name dimensions_id
78 schema:value pub.1104398298
79 rdf:type schema:PropertyValue
80 Naddfc48a0d3c4c5391499d54db853acf rdf:first sg:person.010630315233.97
81 rdf:rest Ncab5adac2cf24cb789f879669d6dda6e
82 Ncab5adac2cf24cb789f879669d6dda6e rdf:first sg:person.012503363065.66
83 rdf:rest rdf:nil
84 Nd1e01ea426d849c5b8d679907fbaed82 schema:volumeNumber 3
85 rdf:type schema:PublicationVolume
86 Nd79d37b347344f57a74e0d266cab1d48 schema:name doi
87 schema:value 10.1186/s41546-018-0032-0
88 rdf:type schema:PropertyValue
89 Nd9db7ce09c2249769cbd35a5a16a6a3d schema:issueNumber 1
90 rdf:type schema:PublicationIssue
91 Neae5e119e5cb4c7abe4bcb8cde987a8c schema:name Springer Nature - SN SciGraph project
92 rdf:type schema:Organization
93 anzsrc-for:15 schema:inDefinedTermSet anzsrc-for:
94 schema:name Commerce, Management, Tourism and Services
95 rdf:type schema:DefinedTerm
96 anzsrc-for:1502 schema:inDefinedTermSet anzsrc-for:
97 schema:name Banking, Finance and Investment
98 rdf:type schema:DefinedTerm
99 sg:journal.1290466 schema:issn 2095-9672
100 2367-0126
101 schema:name Probability, Uncertainty and Quantitative Risk
102 schema:publisher American Institute of Mathematical Sciences (AIMS)
103 rdf:type schema:Periodical
104 sg:person.010630315233.97 schema:affiliation grid-institutes:grid.22147.32
105 schema:familyName Faugeras
106 schema:givenName Olivier P.
107 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010630315233.97
108 rdf:type schema:Person
109 sg:person.012503363065.66 schema:affiliation grid-institutes:grid.5963.9
110 schema:familyName Rüschendorf
111 schema:givenName Ludger
112 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012503363065.66
113 rdf:type schema:Person
114 sg:pub.10.1007/978-0-387-68276-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004453686
115 https://doi.org/10.1007/978-0-387-68276-1
116 rdf:type schema:CreativeWork
117 sg:pub.10.1007/978-1-4419-5821-1_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024571704
118 https://doi.org/10.1007/978-1-4419-5821-1_4
119 rdf:type schema:CreativeWork
120 sg:pub.10.1007/978-1-4614-4869-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026538160
121 https://doi.org/10.1007/978-1-4614-4869-3
122 rdf:type schema:CreativeWork
123 sg:pub.10.1007/978-3-642-33590-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009531412
124 https://doi.org/10.1007/978-3-642-33590-7
125 rdf:type schema:CreativeWork
126 sg:pub.10.1007/978-3-662-04790-3_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006470847
127 https://doi.org/10.1007/978-3-662-04790-3_1
128 rdf:type schema:CreativeWork
129 sg:pub.10.1007/978-94-011-3466-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028525555
130 https://doi.org/10.1007/978-94-011-3466-8
131 rdf:type schema:CreativeWork
132 sg:pub.10.1007/b12016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085139445
133 https://doi.org/10.1007/b12016
134 rdf:type schema:CreativeWork
135 sg:pub.10.1007/bf00532047 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035215282
136 https://doi.org/10.1007/bf00532047
137 rdf:type schema:CreativeWork
138 sg:pub.10.1007/bf00532695 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049811624
139 https://doi.org/10.1007/bf00532695
140 rdf:type schema:CreativeWork
141 sg:pub.10.1007/s00780-004-0127-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044827328
142 https://doi.org/10.1007/s00780-004-0127-6
143 rdf:type schema:CreativeWork
144 grid-institutes:grid.22147.32 schema:alternateName Toulouse School of Economics - Université Toulouse 1 Capitole, Manufacture des Tabacs, 21 Allée de Brienne, 31000, Toulouse, France
145 schema:name Toulouse School of Economics - Université Toulouse 1 Capitole, Manufacture des Tabacs, 21 Allée de Brienne, 31000, Toulouse, France
146 rdf:type schema:Organization
147 grid-institutes:grid.5963.9 schema:alternateName Abteilung für Mathematische Stochastik, Albert-Ludwigs University of Freiburg, Eckerstrasse 1, D-79104, Freiburg, Germany
148 schema:name Abteilung für Mathematische Stochastik, Albert-Ludwigs University of Freiburg, Eckerstrasse 1, D-79104, Freiburg, Germany
149 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...