Question

Theang Uiversity of Science and Technology (S points e the total payment is collective risk model, and the te of is How to determine the safety loading RUN for the premium 4 (15 points) Prove that the coefficient of the first three items the Taylor expansion of the cumulant generating Mark a-1,2,3) of k! the O point is the expectation, the variance and the third function A () at central moment of risk X, respectively 3 of 6 HeBLESUGNE Te ed IS better for him X.If w 0. )+frlxo+h) and EX] = X -h)+f+h)2 o) will prefer Y to X. must be convex ( 1.2,5

Answer 1

Seyety loading fer the pansinis givea CLIB) EINT ECX Cniven ECx PeCo) Pse CD) SL CIte) M. ECN Hente

CLEF Kylt) Ct) logELe t X 2 3 tx 21 3Y 3 1 Now log Clta) 2 3 2 tECX t3E Cx 31 +ECX 1 21 X tECXJttE(x 2! HE3 ECK31 3 2 LETK tEI x] tt 2 1 31 2 (LE LETXJ tExtECK 21 31 2 2 2 2 3 6 +2t ECXTEIX2 ECxJECX'] 2 2 EECKJETX + 2 PETX

Date Siphbyng geti tELX1 t2(Erx]ECK]+Ex-tetEx + VELR-3ECK ECK +2 ECXJ tECK] tt Var (X) + t ΣΤ 3 1 Thind Cantral Monent Paond