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METODOLOG ÍAS Y PRÁCTICAS EN RESERVAS TÉCNICAS PARA SEGUROS DE SALUD Y SEGUROS GENERALES LIMA – 31 DE MAYO, 2007 APESE

METODOLOG ÍAS Y PRÁCTICAS EN RESERVAS TÉCNICAS PARA SEGUROS DE SALUD Y SEGUROS GENERALES LIMA – 31 DE MAYO, 2007 APESEG Presentado por: APESEG & Milliman, Inc. ■ Basic Methods for Evaluating Reserves ■. LOSS RESERVING METHODS. In practice, many methods estimate “Ultimate Losses”

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METODOLOG ÍAS Y PRÁCTICAS EN RESERVAS TÉCNICAS PARA SEGUROS DE SALUD Y SEGUROS GENERALES LIMA – 31 DE MAYO, 2007 APESE

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  1. METODOLOGÍAS Y PRÁCTICAS EN RESERVAS TÉCNICAS PARA SEGUROS DE SALUD Y SEGUROS GENERALES LIMA – 31 DE MAYO, 2007 APESEG Presentado por: APESEG & Milliman, Inc. ■ Basic Methods for Evaluating Reserves■

  2. LOSS RESERVING METHODS • In practice, many methods estimate “Ultimate Losses” • Loss Reserves are Obtained By Subtraction Estimated Ultimate Losses Paid to date Losses Total Reserve - = IBNR Reserve Total Reserve Case Reserve = -

  3. LOSS RESERVING METHODS • Expected Loss (Loss Ratio) • Loss Development (Chain Ladder) • Tail Factors • Inflation Adjustments • Bornhuetter-Ferguson • Generalized Cape Cod • Many, many others available

  4. BASIC METHODS – BASEBALL EXAMPLE • Given the following information, how many homeruns will Sammy Sosa finish with in the 2007 season? • 2004 total homeruns: 40 • 2005 total homeruns: 35 • 2006 total homeruns: 45 • 2007: 20 homeruns through 40 games of the 160 game season

  5. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season?

  6. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season? • Based on the prior 3 years, the Expected Value would be 40 homeruns.

  7. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season?

  8. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season?

  9. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season? • What is the Bornhuetter-Ferguson (B-F) Method? • Named after paper written by Ron Bornhuetter and Ron Ferguson published in the Casualty Actuarial Society Proceedings 1972. • Compromise between the Expected Loss and Loss Development Methods.

  10. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season? • What data is needed for the B-F Method? • Expected Ultimate Value (40) • Factor to Project Actual Data to Ultimate (4.000) • Actual Data to Date (20)

  11. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season? B-F Projection: Ultimate Value = (Expected Value*IBNR Factor)+(Inc. to Date) • IBNR Factor = 1.000 - (1.000/LDF) = 1.000 - (1.000/4.000) = .75 (In Other Words, 75% of the season is left to be played) • Ultimate Value = (40 * .75) + 20 = 50

  12. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season? Expected Value Method Games 0-40 Games 41-80 Games 81-120 Games 121-160 10 Home Runs 10 Home Runs 10 Home Runs 10 Home Runs Development Projection Method Games 0-40 Games 41-80 Games 81-120 Games 121-160 20 Home Runs 20 Home Runs 20 Home Runs 20 Home Runs Bornhuetter-Ferguson Method Games 0-40 Games 41-80 Games 81-120 Games 121-160 20 Home Runs10 Home Runs 10 Home Runs 10 Home Runs

  13. BASIC METHODS – BASEBALL EXAMPLE • How many homeruns will Sammy Sosa finish with in the 2007 season?

  14. BASIC METHODS – BASEBALL EXAMPLE • Comparison of Methods If Actual 10 After 40 Games If Actual 5 After 40 Games If Actual 20 After 40 Games

  15. LOSS RESERVING METHODS • Each Method is Based on Idealized Model of Reality • Models have Implicit Assumptions • Such Assumptions are Rarely Satisfied • No single method or “Formula” will work • Use multiple methods • Use judgment in selecting values • Actuary to test Assumptions • Review Diagnostics • Possibly Use Additional Methods to “Adjust” Data

  16. LOSS RATIO METHODS Expected Loss Ratio E(LR) Earned Premium Ultimate Losses x = • Problem. I know the earned premium, but how do I estimate the Expected Loss Ratio? • Use Pricing Assumptions • Use Available Industry Information • Useful when Company does not have relevant information to analyze • New Business • Small Volume • Late Reporting of Losses (e.g., high excess of loss).

  17. EXPECTED LOSS RATIO METHOD

  18. EXPECTED LOSS METHOD EXAMPLE

  19. DEVELOPMENT METHOD • Also Called the Chain Ladder Method and the Completion Factor Method • Data Triangles • Paid Loss • Incurred Loss • Claim Counts

  20. TRIANGLE EXAMPLE

  21. TRIANGLE EXAMPLE

  22. LOSS DEVELOPMENT METHOD EXAMPLE

  23. “TAIL” FACTORS • Previous Example Showed Development to 60 Months • Suppose Process is Not Complete • Curve Fits • Industry Information • Paid to Incurred Ratios • Judgment

  24. LOSS DEVELOPMENT METHOD EXAMPLE

  25. LOSS DEVELOPMENT METHOD EXAMPLE

  26. IMPORTANCE OF “TAIL” FACTOR

  27. IMPORTANCE OF “TAIL” FACTOR

  28. PAYMENT/REPORTING PATTERNS

  29. EXAMPLE PAYMENT PATTERNS

  30. EMERGENCE AND SETTLEMENT PATTERNS

  31. BRINGING RESULTS TOGETHER • Make Tentative Selections • Loss Development Factors • Tail Factors • Expected Loss Ratios • Generalized Cape Cod Trend and Decay • Weights for Various Methods

  32. BRINGING RESULTS TOGETHER

  33. BRINGING RESULTS TOGETHER

  34. BRINGING RESULTS TOGETHER • Check Ultimate Losses for Reasonableness by Reviewing additional Diagnostics • Ultimate Loss Ratios • Frequency and Severity • Percent of Total Loss by Year • Paid, Case Reserve, IBNR • Ratios of Ceded Reserves to Total Reserves • Average Hindsight Outstanding Cost Per Open Claim • Many Others • Sensitivity Test • Reasonable Ranges for Key Selections

  35. BRINGING RESULTS TOGETHER

  36. BRINGING RESULTS TOGETHER

  37. BRINGING RESULTS TOGETHER

  38. BRINGING RESULTS TOGETHER

  39. BASIC METHODS REVIEW • Basic Methods • Expected Loss • Loss Development • Bornhuetter-Ferguson • Cape Cod • Reasonability and Sensitivity of Estimates • Tail Factor Selection • Review of resulting Ultimate Loss Ratios, Claim Severities and Frequencies, and other Diagnostics • Sensitivity of Results to Key Assumptions • Loss Adjustment Expenses • Documentation

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