Mack (1994)

Question 1

What makes confidence intervals appealing?

Answer 1

• Estimated ultimate claims are not an exact forecast of the true ultimate
• Allows the inclusion of business policy by using a specific confidence probability
• Allows comparison between CL method and other reservin procedures

Question 2

Notation Mack (1994)

Answer 2

• C_ik= cumulative claims amount of AY i through development year k
• C_iI= ultimate claims amount for AY i
• R_i= outstanding claims reserve for AY i
• f_k= age to ae factors

Question 3

Outstanding Claims Reserve

Answer 3

• R_i=C_iI - C_i,I+1-i

Question 4

Ultimate Claims Amount

Answer 4

• C^(hat)_iI=[C^(hat)_i,I+1-i]*[f^(hat)_I+1-i…f^(hat)_I-1 ]

Question 5

Age-to-Age Factors

Answer 5

• f^(hat)_k = [Σ_{j=1 to I-k}(C_j,K+1)]/ [Σ _{j=1 to I-k}(C_jk)]
• Since age to age factors differ from AY to AY, f_k is considered a random deviation from the true factor of increase from C_ik to C_i,k+1

Question 6

Chain Ladder Method in Stochastic Terms

Answer 6

• E[C_i,k+1|C_i1,…,C_ik]=C_ikf_k
• CL makes implicit assumption that the info in C_i,I+1-1 cannot be augment by using other C_ik
• Major consequence of assumption is that it assumes development factors are uncorrelated
• Means that expected size of claims is same after high or low value
• Should not apply CL method to business where we usually observe a small increase in most recent years if past years are higher than usual