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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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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


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, Volume 24, Issue 1/2006, Pages 153–171, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.2006.24.1.153.

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