TY - JOUR
T1 - Risk capital allocation with autonomous subunits
T2 - the Lorenz set
AU - Hougaard, Jens Leth
AU - Smilgins, Aleksandrs
PY - 2016
Y1 - 2016
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
VL - 67
SP - 151
EP - 157
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -