عنوان انگلیسی مقاله:
Is the inf-convolution of law-invariant preferences law-invariant?
ترجمه فارسی عنوان مقاله:
آیا عدم محکومیت حق انتخاب بدون تغییر قانون است؟
Sciencedirect - Elsevier - Insurance: Mathematics and Economics, 91 (2020) 144-154: doi:10:1016/j:insmatheco:2020:01:004
Peng Liu a, Ruodu Wanga, Linxiao Wei b,∗
We analyze the question of whether the inf-convolution of law-invariant risk functionals (preferences)
is still law-invariant. In other words, we try to understand whether the representative economic agent
(after risk redistribution) only cares about the distribution of the total risk, assuming all individual
agents do so. Although the answer to the above question seems to be affirmative for many examples
of commonly used risk functionals in the literature, the situation becomes delicate without assuming
specific forms and properties of the individual functionals. We illustrate with examples the surprising
fact that the answer to the main question is generally negative, even in an atomless probability space.
Furthermore, we establish a few very weak conditions under which the answer becomes positive.
These conditions do not require any specific forms or convexity of the risk functionals, and they are
the richness of the underlying probability space, and monotonicity or continuity of one of the risk
functionals. We provide several examples and counter-examples to discuss the subtlety of the question
Keywords: Law-invariance | Inf-convolution | Risk sharing | Cumulative prospect theory | Rank-dependent utility