MICA
(Math Is Cool for Actuaries)
As easy As 1 2 3 5
March 31, 2007
Henry Newman
The Navigators Group, Inc.
Agenda
(Everybody’s got one)
• Probability
– Basics
• Coins
• NCAA
– Insurance
• Diminishing returns
– Huh?
– What I mean is…
Probability
• Basics
– Coin flipping
• Fair
• How many heads
– NCAA
• My daughter
• “Fair”
• Insurance
Insurance
• Fortuitous event
• Exchange financial certainty to reduce or
eliminate uncertainty
• Law of large numbers
–1,2,9
– No
• Ships
–
–
–
–
This is a marine session, after all
Probability of sinking = 0.001 (or 0.1%)
1,000 ships
Will it/they sink?
Diminishing Returns
• Wake me when lunch is served.
• Economic concept
– Additional units of input yield less and less
additional output
– Insurance applications
• Agents
• Containers/Vessels
• Underwriters
Diminishing Returns - Assumptions
• Underwriters
–
–
–
–
First
Second
Third
Fourth and subsequent
• Fixed Costs: $200K
• Variable Costs
–
–
–
–
First: $1.0M
Second: $800K
Third: $400K
Fourth et. al.: $0
• Revenue
–
–
–
–
First: $1.5M
Second: $1.2M
Third: $700K
Fourth et. al.: $150
Diminishing Returns - Answer
• Underwriter # 1
– Costs = $1.2M; Revenue = $1.5M
– Total Profit = $300K; PUW* = $300K
• Add underwriter # 2
– Costs = $1.2M+$1.0M; Revenue = $1.5M+$1.2M
– Profit = $300K+$200; PUW* = $500K/2 = $250K
* Profit per underwriter
Summary
•
Questions
•Lunch