Credibility Adjusted Predictive Analytics Technique By Goldenson Credibility

Credibility Adjusted Predictive Analytics Technique By Goldenson Credibility Adjusted PA Team Justin Xu, Ethan He, Hukai Luo, Yuchen Wu, Zihan Qin 3/19/2020 1

Outline • Motivation • Objective • Executive Summary • Data Description • Modeling • Final Deliverable • Concluding Remarks 2

Motivation • Current problem: Companies may not have full credibility for prediction • Traditional Credibility techniques have not been formally established when a GLM model is used for prediction • Using a weighted combination of the company and industry prediction may not have a theoretical basis and may not provide consistent and better predictions 3

Objective • Incorporate the traditional actuarial credibility theory and machine learning techniques into the traditional PA techniques in order to improve the prediction power of VA lapse rates 4

Executive Summary • Target Variable: Lapse rate of variable annuities • Model Evaluation Metric: Actual-to-Expected Ratio A/E • Model Design: • Pure Company Model • Credibility Adjusted Company Model Incorporating Industry Data 5

Executive Summary Examples of Comparison of Actual-to-Expected Ratio Company J Duration Pure Company Model Credibility Adjusted Model 1 st Year 88. 24% 93. 43% 2 nd Year 132. 33% 114. 01% 3 rd Year 113. 78% 107. 64% … … … Company B Duration Pure Company Model Credibility Adjusted Model 1 st Year 103. 7% 2 nd Year 93. 72% 99. 76% 3 rd Year 98. 42% … … … Company K Duration Pure Company Model Credibility Adjusted Model 1 st Year 84. 56% 99. 11% 2 nd Year 102. 51% 3 rd Year 91. 67% 94. 18% … … … 6 Notice: The confidence band of A/E is [95%, 105%]. If the pure company model’s A/E falls into this band, there will be no further credibility adjustment.

Data Description ▪ Original Data Set: VA data from Ruark ▪ Training Data: Inforce policies (2012) ▪ Test Data: Inforce policies (2013) 7

Modeling Process • Step 1: Pure Company Model • Split the inforce policy data set by duration • For each calendar year duration, build a GLM model using the company data. • If the A/E ratio falls into the confidence interval [95%, 105%], no further adjustment will be needed • If the A/E ratio falls out of the confidence interval, then go to step 2 8

Modeling Process • Step 2: Credibility Adjusted Model • Use the machine learning technique (decision tree) to split the industry data into different segments (groups) with homogeneous risks for each duration • Build a GLM model for each homogeneous risk group • Calculate credibility factor for each group • Calculate credibility adjusted prediction for each record in each group • Extract the credibility adjusted prediction of company’s records from each group • If the A/E ratio falls out of the confidence interval and is worse than the pure company A/E then use the pure company A/E 9

Illustration of Credibility Adjusted Predictive Model 10

Modeling Process – Special Case • If the A/E ratio falls out of the confidence interval and is worse than the pure company A/E then use the pure company A/E • This could occur for the following combination of reasons • Insufficient number of observations for the company • The company’s lapse rate is significantly different from the industry lapse rate 11

Final Deliverable For each Duration: ● A Specified Grouping/Clustering Criterion ● GLM model for each group ● The Credibility Factor for each group 12

Concluding Remarks • The only model of its kind that combines credibility theory, machine learning and GLM to improve a company’s prediction of its lapse rates • The entire process is automated and could become an important service that Ruark provides to its clients on an annual basis • An individual company would be unable to develop this model on their own because it requires access to industry data as well as the proprietary modeling algorithm developed by the Goldenson Center 13

Thank you! Q&A 14