Risk capital allocation with autonomous subunits: the Lorenz set

Jens Leth Hougaard; Aleksandrs Smilgins

doi:10.1016/j.insmatheco.2015.12.002

Risk capital allocation with autonomous subunits: the Lorenz set

Jens Leth Hougaard, Aleksandrs Smilgins

Sektion for Produktion, Markeder og Politik

5 Citationer (Scopus)

Abstract

Risk capital allocation problems have been widely discussed in the academic literature. We consider a set of independent subunits collaborating in order to reduce risk: that is, when subunit portfolios are merged a diversification benefit arises and the risk of the group as a whole is smaller than the sum of the risks of the individual subunits. The question is how to allocate the risk capital of the group among the subunits in a fair way. In this paper we propose to use the Lorenz set as an allocation method. We show that the Lorenz set is operational and coherent. Moreover, we propose three fairness tests related directly to the problem of risk capital allocation and show that the Lorenz set satisfies all three tests in contrast to other well-known coherent methods. Finally, we discuss how to deal with non-uniqueness of the Lorenz set.

Originalsprog	Engelsk
Tidsskrift	Insurance: Mathematics and Economics
Vol/bind	67
Sider (fra-til)	151–157
Antal sider	7
ISSN	0167-6687
DOI	https://doi.org/10.1016/j.insmatheco.2015.12.002
Status	Udgivet - 1 mar. 2016

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10.1016/j.insmatheco.2015.12.002

Citationsformater

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title = "Risk capital allocation with autonomous subunits: the Lorenz set",

abstract = "Risk capital allocation problems have been widely discussed in the academic literature. We consider a set of independent subunits collaborating in order to reduce risk: that is, when subunit portfolios are merged a diversification benefit arises and the risk of the group as a whole is smaller than the sum of the risks of the individual subunits. The question is how to allocate the risk capital of the group among the subunits in a fair way. In this paper we propose to use the Lorenz set as an allocation method. We show that the Lorenz set is operational and coherent. Moreover, we propose three fairness tests related directly to the problem of risk capital allocation and show that the Lorenz set satisfies all three tests in contrast to other well-known coherent methods. Finally, we discuss how to deal with non-uniqueness of the Lorenz set.",

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T2 - the Lorenz set

AU - Hougaard, Jens Leth

AU - Smilgins, Aleksandrs

PY - 2016/3/1

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N2 - Risk capital allocation problems have been widely discussed in the academic literature. We consider a set of independent subunits collaborating in order to reduce risk: that is, when subunit portfolios are merged a diversification benefit arises and the risk of the group as a whole is smaller than the sum of the risks of the individual subunits. The question is how to allocate the risk capital of the group among the subunits in a fair way. In this paper we propose to use the Lorenz set as an allocation method. We show that the Lorenz set is operational and coherent. Moreover, we propose three fairness tests related directly to the problem of risk capital allocation and show that the Lorenz set satisfies all three tests in contrast to other well-known coherent methods. Finally, we discuss how to deal with non-uniqueness of the Lorenz set.

AB - Risk capital allocation problems have been widely discussed in the academic literature. We consider a set of independent subunits collaborating in order to reduce risk: that is, when subunit portfolios are merged a diversification benefit arises and the risk of the group as a whole is smaller than the sum of the risks of the individual subunits. The question is how to allocate the risk capital of the group among the subunits in a fair way. In this paper we propose to use the Lorenz set as an allocation method. We show that the Lorenz set is operational and coherent. Moreover, we propose three fairness tests related directly to the problem of risk capital allocation and show that the Lorenz set satisfies all three tests in contrast to other well-known coherent methods. Finally, we discuss how to deal with non-uniqueness of the Lorenz set.

U2 - 10.1016/j.insmatheco.2015.12.002

DO - 10.1016/j.insmatheco.2015.12.002

M3 - Journal article

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VL - 67

SP - 151

EP - 157

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

ER -

Risk capital allocation with autonomous subunits: the Lorenz set

Abstract

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