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Understanding Probability and Diminishing Returns in Insurance

Join Henry Newman from The Navigators Group, Inc. for an insightful session on key concepts of probability and diminishing returns in the context of insurance. Explore foundational principles, such as the law of large numbers and fair outcomes, using relatable examples like coin flipping and NCAA scenarios. Understand how diminishing returns apply to insurance cost structures and profitability. This engaging presentation provides valuable insights into underwriting decisions and risk assessment, making complex ideas accessible and relevant.

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Understanding Probability and Diminishing Returns in Insurance

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Presentation Transcript

  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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