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# Modelling Non-Life Insurance

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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!

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### 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