TY - JOUR
T1 - Convex ordering for insurance preferences
AU - Cheung, Ka Chun
AU - Chong, Wing Fung
AU - Yam, Sheung Chi Phillip
PY - 2015/9
Y1 - 2015/9
N2 - In this article, we study two broad classes of convex order related optimal insurance decision problems, in which the objective function or the premium valuation is a general functional of the expectation, Value-at-Risk and Average Value-at-Risk of the loss variables. These two classes of problems include many existing and contemporary optimal insurance problems as interesting examples being prevalent in the literature. To solve these problems, we apply the Karlin–Novikoff–Stoyan–Taylor multiple-crossing conditions, which is a useful sufficient criterion in the theory of convex ordering, to replace an arbitrary insurance indemnity by a more favorable one in convex order sense. The convex ordering established provides a unifying approach to solve the special cases of the problem classes. We show that the optimal indemnities for these problems in general take the double layer form.
AB - In this article, we study two broad classes of convex order related optimal insurance decision problems, in which the objective function or the premium valuation is a general functional of the expectation, Value-at-Risk and Average Value-at-Risk of the loss variables. These two classes of problems include many existing and contemporary optimal insurance problems as interesting examples being prevalent in the literature. To solve these problems, we apply the Karlin–Novikoff–Stoyan–Taylor multiple-crossing conditions, which is a useful sufficient criterion in the theory of convex ordering, to replace an arbitrary insurance indemnity by a more favorable one in convex order sense. The convex ordering established provides a unifying approach to solve the special cases of the problem classes. We show that the optimal indemnities for these problems in general take the double layer form.
U2 - 10.1016/j.insmatheco.2015.06.005
DO - 10.1016/j.insmatheco.2015.06.005
M3 - Article
SN - 0167-6687
VL - 64
SP - 409
EP - 416
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -