This document discusses modelling techniques for a virtual non-life insurance company called Feldafinger Brandkasse using a deterministic and stochastic approach. It describes modelling the company's claims, reserves, assets, reinsurance, and underwriting risks. A DFA (dynamic financial analysis) model is created to simulate the company's economic results over time taking various risks into account. The model calculates required capital (RBC) and shows the company achieving a positive economic result of 5.9 million euros. Risks are aggregated and allocated to different business lines and the company level.

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. 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

4. Modelling non-life insurance

5. Corporate planning
- A deterministic approach -

6. Modelling non-life insurance

7. Corporate planning

8. Corporate planning

9. Corporate planning

10. Corporate planning
number of contracts

11. Corporate planning

12. Corporate planning
= costs of the claims managment

13. Corporate planning

14. Corporate planning
reserves that are estimated
when claims are reported

15. Corporate planning

16. Corporate planning

17. Corporate planning

18. Corporate planning

19. Corporate planning

20. Modelling a company
- A stochastic approach -

21. Modelling non-life insurance

22. Modelling non-life insurance
Economic result function
= technical cash-flow

23. 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.

24. Modelling non-life insurance

25. Modelling non-life insurance

26. Modelling of claims

27. Modelling non-life insurance

28. Modelling non-life insurance
Claims modelling
It is useful to cluster claims in
•Attritional
•Large
•CAT
claims with regard to modelling

29. Modelling non-life insurance
Stochastic modelling of claims

30. Modelling non-life insurance

31. Modelling of attritional claims (MTPL)
-on Ultimate Basis –
Comment: „Ultimate Basis“ means that the final payments of claims
are considered

32. Modelling non-life insurance
Modelling attritional claims (MTPL)

33. Modelling non-life insurance
Modelling attritional claims (MTPL)

34. Modelling non-life insurance
Separate modelling of claims frequeny and claims severity

35. Modelling non-life insurance
Modelling of attritional claims frequency (1/3)

36. Modelling non-life insurance
Modelling of attritional claims frequency (2/3)

37. Modelling non-life insurance
= 64,2 x 378.610
Modelling of attritional claims frequency (3/3)

38. Modelling non-life insurance
Modelling of attritional claims average (1/2)

39. Modelling non-life insurance
Modelling of attritional claims average (2/2)

40. Modelling non-life insurance
not presented
in this lecture
= 2820 x 24,3
Result: Modelling of attritional claims incurred in 2006

41. Modelling large claims (MTPL)

42. Modelling non-life insurance
Modelling large claims

43. Modelling non-life insurance
Modelling large claims

44. Modelling non-life insurance
over 3 years

45. Modelling non-life insurance

46. Modelling non-life insurance
(for 1 mio exposure)
backtesting:
3,3 = 8,8 x 0,371
number of claims
= 8,8 x 378

47. Modelling non-life insurance
Modelling of large claims severity

48. Modelling non-life insurance
= 3,3 x 1,919

49. Modelling Building/CAT claims

50. Modelling non-life insurance

51. Modelling non-life insurance

52. Modelling non-life insurance
Modelling CAT claims

53. Modelling non-life insurance
Modelling CAT claims

54. Modelling non-life insurance
Modelling CAT claims

55. Modelling non-life insurance

56. DFA model
„Feldafinger Brandkasse“

57. DFA model

58. DFA model
DFA = Dynamic Financial Analysis

59. DFA model

60. DFA model

61. DFA model
DFA models are rather complex
because of many simulations and
many LOB and difficult to handle

62. DFA model

63. DFA model
following corporate
planning

64. DFA model
Expected claims (total):
68,5 + 3,3x1,9 18= 74,8
see above
Distribution of severity losses CAT risks
CAT losses

65. RBC ( = Risk Based Capital) calculation
within DFA
Comment: RBC stands for the required capital; in Solvency II it is
named SCR (Solvency Capital Requirement)

66. DFA model

67. DFA Model
Risk aggregation
within Solvency II
Source: DAV-CERA Modul, Klassifizierung und Modellierung von Risiken
defaultmarket underwriting 1.aggregation
2. aggregation

68. DFA model

69. DFA model
RBC = TVAR - Mean

70. DFA model

71. DFA model

72. DFA model

73. DFA model
(building)

74. DFA model

75. DFA model

76. DFA model

77. DFA model
Reserving risk

78. DFA model

79. DFA model

80. DFA model
Economic result: + 5,9 Mio €

81. DFA model
(RBC)

82. DFA model
Results on Company level
TVaR allocation method

83. DFA model
(before RI and CoC)

84. 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.

85. DFA model

86. 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.

87. DFA model
+ 0,2 (gross) minus reinsurance
effect of - 1,5 = -1,3
(assets)

88. Thank you for your attention !
Prof. Dr. Martin Balleer
European Actuarial Academy GmbH
Georg-August-Universität Göttingen
Germany
martin.balleer@actuarial-academy.com