Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Modelling Non-Life Insurance

651 views

Published on

Prof. Dr. Martin Balleer.

Presentation "Modelling Non-Life Insurance" on the open lecture at Taras Shevchenko National University of Kyiv, 18.04.2016.

Thanks to prof. dr. Martin Balleer for kind permission to publish the presentation!

Published in: Education
  • Be the first to comment

Modelling Non-Life Insurance

  1. 1. Modelling Non-Life Insurance Case study: Modelling a (virtual) non-life insurance company « Feldafinger Brandkasse», developed 2006 by German Actuarial Association (DAV) for the needs in education and training Prof. Dr. Martin Balleer Georg-August-Universität Göttingen Germany European Actuarial Academy GmbH
  2. 2. Agenda •Structure of a DFA-model (deterministic and stochastic approach) of a non-life insurance company •Analysis of a virtual non-life company with two business lines (MTPL, building insurance) •Modelling techniques and results for claims, reserve risks, asset risk, reinsurance, underwriting risks
  3. 3. Modelling non-life insurance
  4. 4. Corporate planning - A deterministic approach -
  5. 5. Modelling non-life insurance
  6. 6. Corporate planning
  7. 7. Corporate planning
  8. 8. Corporate planning
  9. 9. Corporate planning number of contracts
  10. 10. Corporate planning
  11. 11. Corporate planning = costs of the claims managment
  12. 12. Corporate planning
  13. 13. Corporate planning reserves that are estimated when claims are reported
  14. 14. Corporate planning
  15. 15. Corporate planning
  16. 16. Corporate planning
  17. 17. Corporate planning
  18. 18. Corporate planning
  19. 19. Modelling a company - A stochastic approach -
  20. 20. Modelling non-life insurance
  21. 21. Modelling non-life insurance Economic result function = technical cash-flow
  22. 22. Modelling non-life insurance The distribution functions of claims of a single risk are known. In order to calculatie the distribution function of the whole portfolio the individual functions have to get aggregated under the assumption that the risks are independent from another.
  23. 23. Modelling non-life insurance
  24. 24. Modelling non-life insurance
  25. 25. Modelling of claims
  26. 26. Modelling non-life insurance
  27. 27. Modelling non-life insurance Claims modelling It is useful to cluster claims in •Attritional •Large •CAT claims with regard to modelling
  28. 28. Modelling non-life insurance Stochastic modelling of claims
  29. 29. Modelling non-life insurance
  30. 30. Modelling of attritional claims (MTPL) -on Ultimate Basis – Comment: „Ultimate Basis“ means that the final payments of claims are considered
  31. 31. Modelling non-life insurance Modelling attritional claims (MTPL)
  32. 32. Modelling non-life insurance Modelling attritional claims (MTPL)
  33. 33. Modelling non-life insurance Separate modelling of claims frequeny and claims severity
  34. 34. Modelling non-life insurance Modelling of attritional claims frequency (1/3)
  35. 35. Modelling non-life insurance Modelling of attritional claims frequency (2/3)
  36. 36. Modelling non-life insurance = 64,2 x 378.610 Modelling of attritional claims frequency (3/3)
  37. 37. Modelling non-life insurance Modelling of attritional claims average (1/2)
  38. 38. Modelling non-life insurance Modelling of attritional claims average (2/2)
  39. 39. Modelling non-life insurance not presented in this lecture = 2820 x 24,3 Result: Modelling of attritional claims incurred in 2006
  40. 40. Modelling large claims (MTPL)
  41. 41. Modelling non-life insurance Modelling large claims
  42. 42. Modelling non-life insurance Modelling large claims
  43. 43. Modelling non-life insurance over 3 years
  44. 44. Modelling non-life insurance
  45. 45. Modelling non-life insurance (for 1 mio exposure) backtesting: 3,3 = 8,8 x 0,371 number of claims = 8,8 x 378
  46. 46. Modelling non-life insurance Modelling of large claims severity
  47. 47. Modelling non-life insurance = 3,3 x 1,919
  48. 48. Modelling Building/CAT claims
  49. 49. Modelling non-life insurance
  50. 50. Modelling non-life insurance
  51. 51. Modelling non-life insurance Modelling CAT claims
  52. 52. Modelling non-life insurance Modelling CAT claims
  53. 53. Modelling non-life insurance Modelling CAT claims
  54. 54. Modelling non-life insurance
  55. 55. DFA model „Feldafinger Brandkasse“
  56. 56. DFA model
  57. 57. DFA model DFA = Dynamic Financial Analysis
  58. 58. DFA model
  59. 59. DFA model
  60. 60. DFA model DFA models are rather complex because of many simulations and many LOB and difficult to handle
  61. 61. DFA model
  62. 62. DFA model following corporate planning
  63. 63. DFA model Expected claims (total): 68,5 + 3,3x1,9 18= 74,8 see above Distribution of severity losses CAT risks CAT losses
  64. 64. RBC ( = Risk Based Capital) calculation within DFA Comment: RBC stands for the required capital; in Solvency II it is named SCR (Solvency Capital Requirement)
  65. 65. DFA model
  66. 66. DFA Model Risk aggregation within Solvency II Source: DAV-CERA Modul, Klassifizierung und Modellierung von Risiken defaultmarket underwriting 1.aggregation 2. aggregation
  67. 67. DFA model
  68. 68. DFA model RBC = TVAR - Mean
  69. 69. DFA model
  70. 70. DFA model
  71. 71. DFA model
  72. 72. DFA model (building)
  73. 73. DFA model
  74. 74. DFA model
  75. 75. DFA model
  76. 76. DFA model Reserving risk
  77. 77. DFA model
  78. 78. DFA model
  79. 79. DFA model Economic result: + 5,9 Mio €
  80. 80. DFA model (RBC)
  81. 81. DFA model Results on Company level TVaR allocation method
  82. 82. DFA model (before RI and CoC)
  83. 83. DFA Model Return = Turnover Profit / Loss (balance sheet) Classical Turnover Orientation • Profit Turnover-Ratio Risk CapitalRisk Capital Economic Result Value and Risk Oriented (Economical View on Return and Risk) • Return on Risk Adjusted Capital (RORAC) Source: Diers, Interne Unternehmensmodelle, ifa-Verlag Ulm, Germany Management reacted to the altered prevailing conditions with a paradigm shift in corporate strategy developing from classical turnover orientation to value and risk based management in economic terms.
  84. 84. DFA model
  85. 85. DFA Model Risk margin: Cost of Capital Background: MVM is the risk premium for an investor who has to finance risk capital; r(t) is risk free rate, CoC is the spread.
  86. 86. DFA model + 0,2 (gross) minus reinsurance effect of - 1,5 = -1,3 (assets)
  87. 87. Thank you for your attention ! Prof. Dr. Martin Balleer European Actuarial Academy GmbH Georg-August-Universität Göttingen Germany martin.balleer@actuarial-academy.com

×