Comparison of Two kinds of Bonus- Malus Systems in Environmental Impairment Liability Insurance
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1 Comparison of Two kinds of Bonus- Malus Systems in Environmental Impairment Liability Insurance YAO Dan, ZHENG Sujin Presented by Dannie Yao Central University of Finance and Economics
2 Outline EIL Insurance in China BMS applied to EIL Insurance Analysis to BMS Conclusion and Recommendation
3 EIL Insurance in China 1990s Started a pilot in the 1990s, but withdrawn from the market soon; In 2007, EPA and CIRC published the Guidelines on Environmental impairment liability Insurance work ; In 2013, EPA and CIRC jointly issued "Guidance on conducting mandatory Environmental impairment liability Insurance pilot work".
4 Bonus-Malus System A rate adjustment system, mainly used in non-life Insurance practice; Most common in automobile insurance and also called No Claim Discount System (NCD) in China; Should the BMS be introduced to EIL insurance policy?
5 Bonus-Malus System Add a BMS into EIL insurance is practicable: The current premium of EIL insurance is relatively high; On China's current market, EIL insurance only covers accidental environmental pollution accident; For EIL insurance, the risk of insured is really different; The high premium has already been a problem in the promotion of EIL insurance.
6 Outline EIL Insurance in China BMS applied to EIL Insurance Analysis to BMS Conclusion and Recommendation
7 BMS Applied to EIL Insurance Based on number of claims The renewal premium is adjusted according to the number of claims. Claim number is the only influence factor of premium level transfer. Based on Loss ratio The renewal premium is adjusted according to the loss ratio. Claim number and loss amount are all influence factors.
8 BMS Applied to EIL Insurance Based on number of claims Premiums are divided into seven levels, the corresponding adjustment factors of each level are 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, policyholders premiums equal to the basic premium multiple adjustment factor. If a claim happened in this year, the adjustment factor for the next year raised one level; if the insured event did not occur for two consecutive years, and then adjust factor decline one level. The adjustment factor is limited by the minimum and maximum level.
9 BMS Applied to EIL Insurance Based on loss ratio Premiums are divided into four levels, the corresponding adjustment factors of each level are 0.9, 1, 1.1, 1.3, policyholders premiums equal to the basic premium multiple adjustment factor. Loss ratio 30%, decline one level; 30% < loss ratio 60%, remain original level; 60% < loss ratio 120%, increase one level; Loss ratio >120%, increase two levels. The adjustment factor is limited by the minimum and maximum level.
10 Assumption to Transfer matrix Claim frequency follows N (0, 1) distribution. The occurrence probability is p. Claim amount follows a truncated exponential distribution with a parameter θ=73.5. The safe factor of premium is 40%. The gross premium of an EIL policy is (Unit: 10 thousand CNY): G=E(S)(1+c)=E(X)P(N=1)(1+c)=
11 Transfer matrix BMS based on number of claims Q = Through calculation, the steady-state distribution is: π = ( )
12 Transfer matrix BMS based on loss ratio Q = Through calculation, the steady-state distribution is: π = ( )
13 Outline EIL Insurance in China BMS applied to EIL Insurance Analysis to BMS Conclusion and Recommendation
14 Analysis to BMS We choose five indicators to analyze the Bonus-Malus system: The Relative Stationary Average Premium Level, (RSAL) The coefficient of variation of the insured premium, (CV) The efficiency of Bonus-malus system (Eff Loi ) Implicit punishment for new policyholders (IPN) Index of toughness (T)
15 Analysis to BMS The Relative Stationary Average Premium Level RSAL = Average premium in steady state Minimum premium level Maximum premium level Minimum premium level BMS based on number of claims RSAL = BMS based on loss ratio RSAL =
16 Analysis to BMS The coefficient of variation of the insured premium CV = Te standard deviation of steady state average premium Te expectation of steady state average premium BMS based on number of claims CV = BMS based on loss ratio CV =
17 Analysis to BMS The efficiency of Bonus-malus system The speed of premium increases along with loss ratio or frequency can be weighted by Elasticity. BMS based on number of claims Eff Loi p = dr p r p dp p = dr p dp p r p =
18 Analysis to BMS BMS based on loss ratio Eff Loi Eη = dr Eη r Eη deη Eη = dr Eη deη Eη r Eη Eη = E S G = E S G pe X = G E X = θ 1 e 190 θ Eη = E S G pθ 1 e = G 190 θ
19 Analysis to BMS Define ε p and ε θ as the elastic based on p and θ. Hold one influence factor (p or θ) as a constant, we can get the elastic based on the other. ε p = dr Eη deη = dr Eη dp deη dp, ε θ = dr Eη deη = dr Eη dθ deη dθ ε p = , ε θ =
20 Analysis to BMS Implicit punishment for new policyholders IPN = Te premium for new policyolder Average premium in steady state Average premium in steady state BMS based on number of claims Through calculation, the IPN is BMS based on loss ratio Through calculation, the IPN is
21 Analysis to BMS Index of toughness The importance range of these indicators is: RSAL>Eff Loi > CV > IPN. Their weights are 40%, 30%, 20%, 10%. BMS based on number of claims T = RSAL 40% + Eff Loi 30% + CV 20% + IPN 10% = BMS based on loss ratio T = RSAL 40% + Eff Loi 30% + CV 20% + IPN 10% =
22 Analysis to BMS Name of Index BMS based on loss ratio (1) BMS based on number of claims (2) The one more severe RSAL (1) CV (1) IPN (2) Eff ε p = , ε θ = (2) T (1) IPN and Efficiency might be effected by the discount range other than BMS basis. To get rid of the impact of this reason, we redesign the discount range of BMS based on number of claims.
23 Analysis to BMS Set the discount range as 0.9 to 1.3, the gap between each level and transfer rule are as the same. Name of Index BMS based on loss ratio (1) BMS based on number of claims (2) The one more severe RSAL (1) CV (1) IPN (2) Eff ε p = , ε θ = T (1)
24 Outline EIL Insurance in China BMS applied to EIL Insurance Analysis to BMS Conclusion and Recommendation
25 Conclusion and Recommendation Loss ratio as a basis of Bonus-malus system is more severe than number of claims, and a higher risk discrimination; Current Bonus-malus systems are all moderate and play a role in promoting the rationalization of premium. Be cautious when set the lowest discount level; Link regular check result of the Environmental Protection Agency (EPA) to premium discount level.
26 Thank You
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