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MICA ( M ath I s C ool for A ctuaries)

MICA ( M ath I s C ool for A ctuaries). 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

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MICA ( M ath I s C ool for A ctuaries)

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  1. MICA(Math Is Cool for Actuaries) As easy As 1 2 3 5 March 31, 2007 Henry Newman The Navigators Group, Inc.

  2. Agenda(Everybody’s got one) • Probability • Basics • Coins • NCAA • Insurance • Diminishing returns • Huh? • What I mean is…

  3. Probability • Basics • Coin flipping • Fair • How many heads • NCAA • My daughter • “Fair” • Insurance

  4. 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?

  5. 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

  6. 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 - Assumptions

  7. 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

  8. Summary • Questions • Lunch

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