Session 2 Motor Insurance Pricing George Kau, FSA Victor Khong - PDF document

SOA Big Data Seminar 13 Nov. 2018 | Jakarta, Indonesia Session 2 Motor Insurance Pricing George Kau, FSA Victor Khong

11/20/2018 SOA Big Data Seminar Motor Insurance Pricing George Kau FSA, FASM Victor Khong KPMG PLT Nicholas Actuarial Solutions 13 November 2018 Brief Introduction of Motor Insurance Rating in Malaysia 2

11/20/2018 Motor Insurance – Basic Cover Motor Insurance in Malaysia is renewed yearly Premiums are paid before insurance coverage starts Death or injury Damage to other to other parties parties’ property (TPBI) (TPPD) Third Party Cover Own loss due to theft or fire Third Party Fire and Theft Cover Own damage to vehicle due to Comprehensive Cover accident (OD) 3 Motor Insurance – Extension Cover Additional perils can be added to the policy with additional premiums Flood, earthquake, hurricane, Breakage of glass in windscreen landslide or windows Additional named driver Strike, riot and civil commotion Liability of passengers for acts Passenger liability of negligence Additional business use Tuition and testing purposes 4

11/20/2018 Motor Tariff ‐ Rating Factors Premium rates charged by insurance companies were ranging within the allowable loading limit of Motor Tariff. Sum insured Engine capacity of vehicle Rating factors set out in the motor tariff Region such as West and East Malaysia Loadings for age of driver, age of vehicle and past claims history 5 Liberalization of Motor Tariff ‐ Additional Rating Factors General insurance companies began to use Generalized Linear Model (GLM) in self motor insurance rating Safety features Premiums Vehicle make Additional determined after rating liberalization factors Gender of driver of motor tariff Experience of driver 6

11/20/2018 Process of Building a Generalized Linear Model 1 6 7 Setting Model Specifying Objectives Validation and Model Form and Goals Diagnostics 2 5 8 Select the Model Data Splitting Data Comparison 10 3 4 9 Data Models Process Data Analysis Preparation Selection Improvement 7 GLM – Data Preparation Step 1 ‐ 5 8

11/20/2018 Step 1. Setting Objectives and Goals – Purpose of Modelling What's to predict? Set it as the response variable Quantitative Response Variable Frequency Severity (Claim (Claim Count Amount per Pure Premium per Exposure) Claim Count) 9 Step 2. Select the Data – Risk Factor Vs. Rating Factor e.g. driver’s recklessness Factors that influenced Risk such as drive after alcoholic the risk of Factors drinking will increase the risk vehicle/accident of accident Data availability e.g. value of the vehicle Rating Factors used to is a rating factor; higher the Factors determine the rating sum insured, the higher the premium 10

11/20/2018 Step 2. Select the Data (cont’d) – Driver Factor Category Rating Factor Description Data Structure Age of Driver Age of vehicle owner, or age of Integer policyholder Driving Length of driving period or Experience Integer Experience Driving Record Number of traffic offences or bad Integer record Gender Male or Female Categorical Marital Status Single or Married Categorical Number of Driver List of drivers in the policy Integer 11 Step 2. Select the Data (cont’d) – Vehicle Factor Category Rating Factor Description Data Structure Cubic Capacity Dimension of vehicle engine Integer Manufactured Number of years since the vehicle is Integer Year manufactured Safety Features Number of safety installations Integer Odometer Distance travelled by the vehicle Numerical Vehicle Type Sports or Normal vehicle Categorical 12

11/20/2018 Step 2. Select the Data (cont’d) – Location Factor Category Rating Factor Description Data Structure Region East or West Malaysia Categorical Address Location Postcode Categorical Urbanization City, rural and suburban Categorical Level 13 Step 2. Select the Data (cont’d) – Policy Factor Category Rating Factor Description Data Structure Sum Insured Market value or agreed value of the Numerical vehicle Policy Coverage Type of coverages Categorical Renewal New business or renewal Business Categorical Indicator Claim Count Number of claim incurred in the past Integer Experience Claim Amount Amount of claim incurred in the past Numerical Experience No Claim Discount offered for good driving Numerical Discount (NCD) record 14

11/20/2018 Step 3. Data Preparation – Merging and Consideration Location Policy Vehicle Consideration before merging NCD Claim unique key time period Client for matching ETL process data unknown aggregation risk factors master database 15 Step 3. Data Preparation (cont’d) – Merging and Consideration categorical data numerical data outliers are excluded missing data 16

11/20/2018 Step 4. Data Analysis – Reserving vs Rating Peril (Type of Loss) Motor Act TPBI OD TPPD Motor Others Fire & Theft PRAD IBNR IBNR Cross‐Reference PRICING RESERVING DATA Reported Reported DATA Checking Claims Claims 17 Step 4. Data Analysis (cont’d) – Correlation Plot Correlation Plot – Pearson Coefficient Correlation Method Can you find the dependent predictors ? 18

11/20/2018 Step 4. Data Analysis (cont’d) – Relationship Pattern Plot Relationship Pattern Plot Sum insured and gross premium are closely related, suggest to drop gross premium as predictor 19 Step 5. Data Splitting – Training and Validation Sets Training Set ( 70% ) to BUILD the GLM model using rating factors Validation Set ( 30% ) to REFINE the GLM model 20

11/20/2018 GLM ‐ Modelling Step 6 ‐ 9 21 Generalized Linear Model ‐ Response variable Regression analysis is a form predictive modeling technique which investigates the relationship between a response variable � and the predictors � � � � � � � � � � � � � � � � ⋯ � � � � � � � Specifies the explanatory Response Locatio variables � � , � � , … � � in Policy Vehicle n variable the model NC Claim D Client Master Database 22

11/20/2018 Generalized Linear Model (cont’d) ‐ Response variable Continuous Response Variables Inverse Gaussian / e.g. severity, net premium Gamma Regression Count Response Variables Poisson / Negative e.g. claim count Binomial Regression Categorical Response Variables Binomial/Logistic e.g. fraud, lapse (yes or no) Regression 23 Generalized Linear Model (cont’d) ‐ Response variable Gamma distribution v.s. Inverse Gaussian distribution for Severity Model 24

11/20/2018 Generalized Linear Model (cont’d) ‐ Response variable Distribution Typical Uses Support of Distribution Real: ��∞, �∞� Gaussian Linear response data, constant (Normal) increments or decrements Real: �0, �∞� Inverse Positively skewed data with Gaussian distribution’s tail decreases slowly Real: �0, �∞� Gamma Exponential response data, increase or decrease with constant ratio Distribution Typical Uses Support of Distribution Integer: 0,1,2 … , N Binomial Single outcome from N occurrences Integer: 0,1,2 … Poisson Count data 25 Generalized Linear Model (cont’d) – Link Function The relationship between the mean of the response variable distribution function and a linear combination set of predictors Numerical example for a Gamma Log Link Model ln � �������� � � � � � � � � � � � � � � ⋯ � � � � � � �������� � � ��� � � � � � � � � � � � � ⋯ � � � � � � � � � � � � � �������� � � 3,000 l� � �������� � � ln 3,000 � 8.01 � �������� � � ��� 8.01 � 3,000 26

11/20/2018 Generalized Linear Model (cont’d) – Link Function Distribution Link Name Link Function, Mean Function �� � ���� �� � � � � �� Normal Identity �� � 1 Inverse Inverse � � ���� �� � � Gaussian Squared � �� � ln ��� Log �� � 1 Gamma Inverse Exponential � � ����� �� � Family �� � ln ��� Log � exp ���� Binomial Logit �� � ln � 1 � �� � � 1 � exp ���� �� � ln ��� � � exp ���� Poisson Log 27 Step 6. Specifying Model Form – Severity Model Example Objective Predict the Expected Severity of Motor Insurance Response Severity = Claim Amount / Claim Count Variable Sum Insured, Underwriting Year, Cubic Capacity of Vehicle, Predictors Manufacturer of Vehicle, Manufactured Year, Region Weights Claim Count Models Inverse Gaussian Distribution or Gamma Distribution Link Function Log Link Inverse Gaussian and Log Link Gamma 28