A.2 PBA Corner

Question 1

VM20 Credibility

2008 VBT vs 2015 VBT

Answer 1

2008 VBT:

• Limit Fluctuation
• Buhlmann
• “other method that follows Actuarial Practice”
• no restrictions on changing methods

2015 VBT:

• Limited fluctuation
• Buhlmann
• Commissioner must approve change in method and demonstrate rationale in support of change

Question 2

Limited Fluctuation method

formula; Adv & disadv

Answer 2

z = min(1, rm / (z * std dev of m)
r = error margin
z = norm distr number associated with p
m = mortality ratio A/E by amount

vm20 requires p >= 95% and r <= 5%

advantages:

• only requires company data
• straightforward calc and inputs. simple/easy

disadvantages:

• Arbitrary r and p
• doesnt consider relation with other companies
• no explicit model or quantity optimized

Question 3

Buhlmann Method

formula; Adv & disadv

Answer 3

z = A / W
W = A  + (1.09B - 1.204C) / 0.019604 A

A = sum[insured amount * exposure * mortality]
B = sum[insured amt^2 * exposure * mortality]
c = sum[insured amt^2 * exposure^2 * mortality]

advantages:

• no parameters to select arbitrarily
• reflects company and industry variance

disadvantages

• harder to explain/interpret
• requires reliance on ‘statistical agents’

Question 4

Outcomes from 2009 Credibility Theory Practices Report

Answer 4

• Buhlmann factor had generally higher credibility

- count and amount basis can be quite different