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