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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year


Cite Score 2016: 0.33

SCImago Journal Rank (SJR) 2016: 0.346
Source Normalized Impact per Paper (SNIP) 2016: 0.167

Mathematical Citation Quotient (MCQ) 2016: 0.32

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2196-7040
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On the optimal risk allocation problem

Christian Burgert / Ludger Rüschendorf
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.2006.24.1.153

SUMMARY

The optimal risk allocation problem or equivalently the problem of risk sharing is the problem to allocate a risk in an optimal way to n traders endowed with risk measures ϱ1, …, ϱn. This problem has a long history in mathematical economics and insurance. In the first part of the paper we review some mathematical tools and discuss their applications to various problems on risk measures related to the allocation problem like to monotonicity properties of optimal allocations, to optimal investment problems or to an appropriate definition of the conditional value at risk. We then consider the risk allocation problem for convex risk measures ϱi. In general the optimal risk allocation problem is well defined only under an equilibrium condition. This condition can be characterized by the existence of a common scenario measure. We formulate ameaningful modification of the optimal risk allocation problem also formarkets without assuming the equilibrium condition and characterize optimal solutions. The basic idea is to restrict the class of admissible allocations in a proper way.

Key words and phrases: Pareto optimal risk allocation; risk sharing; risk measures; equilibrium

About the article

Received: 2005-10-15

Accepted: 2006-02-20

Published Online: 2009-09-25

Published in Print: 2006-07-01


Citation Information: Statistics & Decisions, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.2006.24.1.153.

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Citing Articles

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[1]
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[2]
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[3]
Agustín Santos, Antonio Fernández Anta, José A. Cuesta, and Luis López Fernández
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[4]
Carole Bernard, Franck Moraux, Ludger Rüschendorf, and Steven Vanduffel
Quantitative Finance, 2015, Volume 15, Number 7, Page 1157
[5]
L. Bayón, P.J. García-Nieto, R. García-Rubio, J.M. Grau, M.M. Ruiz, and P.M. Suárez
International Journal of Computer Mathematics, 2016, Volume 93, Number 5, Page 735
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Marco Maggis and Davide La Torre
INFOR: Information Systems and Operational Research, 2012, Volume 50, Number 3, Page 117
[7]
Damir Filipović, Michael Kupper, and Nicolas Vogelpoth
SIAM Journal on Financial Mathematics, 2012, Volume 3, Number 1, Page 402
[8]
Ludger Rüschendorf
Journal of Statistical Planning and Inference, 2009, Volume 139, Number 11, Page 3921
[9]
Beatrice Acciaio and Gregor Svindland
Insurance: Mathematics and Economics, 2009, Volume 44, Number 3, Page 426
[10]
Peng Li, Andrew E.B. Lim, and J. George Shanthikumar
Insurance: Mathematics and Economics, 2010, Volume 47, Number 1, Page 1
[11]
Christian Burgert and Ludger Rüschendorf
Insurance: Mathematics and Economics, 2008, Volume 42, Number 1, Page 177
[12]
Swen Kiesel and Ludger Rüschendorf
Insurance: Mathematics and Economics, 2010, Volume 47, Number 2, Page 167
[13]
Michael Ludkovski and Ludger Rüschendorf
Statistics & Probability Letters, 2008, Volume 78, Number 10, Page 1181
[14]
Christos E. Kountzakis
Mathematics and Financial Economics, 2011, Volume 4, Number 3, Page 223
[15]
Rania Hentati and Jean-Luc Prigent
Statistics & Decisions, 2011, Volume 28, Number 1
[16]
Swen Kiesel and Ludger Rüschendorf
Statistics & Decisions, 2009, Volume 26, Number 4
[17]
Rose Anne Dana and C. Le Van
Mathematical Finance, 2010, Volume 20, Number 3, Page 327
[18]
M. Kaina and L. Rüschendorf
Mathematical Methods of Operations Research, 2009, Volume 69, Number 3, Page 475
[19]
Beatrice Acciaio
Finance and Stochastics, 2007, Volume 11, Number 2, Page 267

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