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MICA(Math Is Cool for Actuaries)
As easy As 1 2 3 5March 31, 2007Henry 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
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