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s: observed claims rate
z: credibility factor
Premium =(1− z)*m+ z * s
Group Life UW and RM Application 36
Pricing
Experience Rating
Assumptions:
• Claims numbers distribution
• Claims size distribution
• Distribution for variation between groups of
similar size and structure
Group Life UW and RM Application 37
Experience Rating
Experience Rating: Examples
• Sums insured: identical
• Claims number: Poisson distribution
• Variation: Gamma distribution
n t
z n t
*
*
+
=
α
n: number of years experience (risk years)
t: expected number of claims
α: parameter of Gamma distribution
Group Life UW and RM Application 38
Experience Rating
Experience Rating: Examples
• Expected claims rate: 2.50 ‰
• Years of experience: 5
• Actual claims rate (burning
cost): 1.50 ‰
• α (parameter of credibility
formula): 10
Size of
Scheme
Credibility
Factor
1) 250 lives 24%
2) 1,000 lives 56%
3) 5,000 lives 86%
Group Life UW and RM Application 39
Experience Rating
Experience Rating: Examples
1) (2.50‰ * 76%) + (1.50‰ + 24%) = 2.26‰
2) (2.50‰ * 44%) + (1.50‰ + 56%) = 1.94‰
3) (2.50‰ * 14%) + (1.50‰ + 86%) = 1.64‰
Group Life UW and RM Application 40
Pricing
Experience Rating
• Unchanged group structure ?
• Constant group size ?
• Unchanged benefit formulas ?
• Unchanged scope of cover ?
A Berkshire Hathaway Company
Activities of Gen Re
Group Life UW and RM Application 42
Activities of Gen Re
Reinsurance
• Quota share basis
• Surplus basis
• Catastrophe Excess of Loss
• Per Head Excess of Loss
Group Life UW and RM Application 43
Activities of Gen Re
Services
• Product design / pricing
• Portfolio analysis
• Quotation service
• Quotation tools
• Training of group underwriters
Group Life UW and RM Application 44
Workshop
Workshop
Group Life UW and RM Application 45
Workshop No 1
Case 1:
• Company A (an airline company) wishes to insure its staff for Group Life Insurance. The
sum insured will be 4 x annual salary.
• The following data has been given on the occupations:
Occupation Numbers Average Salary
Pilots: 100 100,000
Cabin Crew 1,250 25,000
Ground Staff (non-manual) 2,000 20,000
Ground Staff (manual) 1,500 15,000
Group Life UW and RM Application 46
Workshop No 1 (Cont)
It is known that the airline has the following aircraft:
Boeing 747: 2
Boeing 737: 12
Airbus A300: 6
The unadjusted Unit Rate for the whole group has been calculated at 2.50 per 1,000 sum
insured.
• How would you quote for this group?
• Comments?
Group Life UW and RM Application 47
Workshop No 2
Case 2:
Company B is active in the distribution of products. It used to own a manufacturing division
which was sold at the end of 2004. The company has had
a Group Life scheme for its employees for the last 10 years.
The following data on the occupational split is known:
Professional, managerial: 100
Office staff: 750
Drivers and warehouse workers: 250
The claims experience for the group in the last 5 years has been as follows:
Group Life UW and RM Application 48
Workshop No 2 (Cont)
Year: No. Lives Sum Insured No. Claims Tot Claims
1.7.2003 2,700 121,500,000 10 526,095
1.7.2004 2,650 125,960,000 12 646,820
1.7.2005 1,150 74,750,000 2 126,000
1.7.2006 1,075 73,100,000 3 205,000
1.7.2007 1,090 78,480,000 1 110,000
The unadjusted Unit Rate has been calculated as 3.00 per 1,000 sum insured. The total
number of lives is
now 1,100 with a total sum insured of 80,000,000.
• For the credibility factor use the following formula:
• z = Ex / (10 + Ex), where
• Ex: expected claims during period of scheme history = (number of risk years) x (adjusted
Unit Rate)
• How would you quote for this group?
• Comments?
Group Life UW and RM Application 49
The End
Precise and Efficient Static Array Bound Checking for
Large Embedded C Programs
Arnaud Venet
Kestrel Technology
NASA Ames Research Center
Moffett Field, CA 94035
arnaud@email.arc.nasa.gov
Guillaume Brat
Kestrel Technology
NASA Ames Research Center
Moffett Field, CA 94035
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