Factors Driving Duration to Cross-Selling in Non-Life Insurance: New Empirical Evidence from Switzerland
Abstract
:1. Introduction
2. Insurance Portfolio Data and Cross-Selling Statistics
2.1. Time to Cross-Selling
2.1.1. Portfolio Development
2.1.2. Duration to Cross-Selling and Right-Censoring
2.1.3. Kaplan–Meier Estimates for the Cross-Selling Probability
2.2. Covariates and Descriptive Statistics
3. Duration to Cross-Selling Analysis
3.1. Model for the CA Cohort
3.1.1. Cox Model
3.1.2. Model Development
3.1.3. Binning of Continuous Variables
3.1.4. Accelerated Failure Time Model
3.1.5. Numerical Results and Discussion
3.2. Model for the HL Cohort
3.2.1. Model Development
3.2.2. Numerical Results and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
1 | GE includes major cities like Zurich and Winterthur, GW includes Berne and Basel, GA includes St. Gallen, Chur and Lucerne, GR includes Geneva, Lausanne and Sion, and GI includes Lugano and Locarno. We denote categorical variables in bold face and, e.g., the vector GEO has the form (GE, GW, GA, GR, GI, OT). |
2 | We use subscripts CA and HL on to distinguish the premium in both products. |
3 | As we use rounded quartile values as boundaries for the classes, we find shares not exactly equal to 25%. |
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Variable | Description |
---|---|
Customer attributes | |
Age of the policyholder | |
Urbanicity of the residence: urban (UU) or rural (UR) | |
Geographic region of the residence: | |
– East Swiss Plateau (GE) | |
– West Swiss Plateau (GW) | |
– Alps and Prealps (GA) | |
– Romandy (GR) | |
– Italian-speaking area of Switzerland (GI) | |
– Outside of Switzerland (OT) | |
Products attributes | |
CA or HL contract premium paid (in CHF) | |
Number of damages declared (0, 1, 2, 3+) | |
Number of contracts underwritten (1, 2, 3, 4+) | |
Life insurance underwritten (yes or no) | |
Buying channel attribute | |
Access channel used by the policyholder: | |
– Tied agent (TA) | |
– Independent intermediary (IY) | |
– Broker (BR) | |
– Internet/insurer’s website (IT) | |
– Other (OT) |
CA Cohort | HL Cohort | |||||||
---|---|---|---|---|---|---|---|---|
Share | Share | |||||||
Age (AGE, in years) | ||||||||
18–25 | 40 | 189 | 349 | 122 | 412 | 919 | ||
26–40 | 221 | 762 | 1683 | 111 | 423 | 1348 | ||
41–65 | 250 | 781 | n.a | 112 | 365 | 1226 | ||
66+ | 25 | 703 | 1231 | 179 | 853 | n.a. | ||
Urbanicity (URB) | ||||||||
Urban (UU) | 190 | 616 | 1218 | 205 | 849 | n.a. | ||
Rural (UR) | 137 | 416 | 819 | 89 | 289 | 719 | ||
Geographic region () | ||||||||
East Swiss Plateau (GE) | 159 | 509 | 1001 | 122 | 451 | 1168 | ||
West Swiss Plateau (GW) | 118 | 380 | 710 | 126 | 416 | 1156 | ||
Alps and Prealps (GA) | 108 | 365 | 720 | 96 | 325 | 822 | ||
Romandy (GR) | 214 | 609 | 1370 | 153 | 589 | 1641 | ||
Italian-speaking area (GI) | 396 | 1223 | n.a. | 122 | 550 | 1382 | ||
Outside Switzerland (OT) | 179 | 481 | 759 | 34 | 96 | 216 | ||
CA contract premium (PRE, in CHF) | ||||||||
0–747 | 212 | 654 | 1380 | |||||
748–1068 | 137 | 441 | 869 | |||||
1069–1405 | 128 | 404 | 762 | |||||
147 | 418 | 853 | ||||||
HL contract premium (PRE, in CHF) | ||||||||
0–109 | 117 | 397 | 901 | |||||
110–252 | 201 | 868 | n.a. | |||||
253–391 | 112 | 409 | 1233 | |||||
92 | 275 | 699 | ||||||
Number of damages () | ||||||||
0 | 158 | 478 | 955 | 118 | 413 | 1137 | ||
1 | 95 | 365 | 758 | 112 | 349 | 792 | ||
2 | 113 | 365 | 763 | 456 | 820 | n.a. | ||
85 | 314 | 478 | 884 | 1264 | 1264 | |||
Number of contracts () | ||||||||
1 | 479 | 931 | 1774 | 475 | 1207 | n.a. | ||
2 | 3 | 7 | 15 | 3 | 7 | 17 | ||
3 | 6 | 12 | 19 | 4 | 11 | 17 | ||
2 | 7 | 31 | 6 | 8 | 37 | |||
Life insurance underwritten (LIF) | ||||||||
No | 152 | 470 | 933 | 120 | 427 | 1161 | ||
Yes | 40 | 189 | 522 | 92 | 165 | 253 | ||
Access channel () | ||||||||
Tied agent (TA) | 114 | 365 | 708 | 109 | 372 | 977 | ||
Independent intermediary (IY) | 162 | 617 | 1214 | 148 | 462 | 1720 | ||
Broker (BR) | 524 | 1676 | n.a. | 264 | 1343 | n.a. | ||
Internet/insurer’s website (IT) | 144 | 438 | 704 | n.a. | n.a. | n.a. | ||
Other (OT) | 475 | n.a. | n.a. | 112 | 932 | n.a. |
Distribution | Exponential | Weibull | Gamma | Log-Normal |
---|---|---|---|---|
CA cohort | 108,385 | 106,309 | 106,332 | 106,306 |
Cox Model (4) | AFT Model (6) | |||||||
---|---|---|---|---|---|---|---|---|
exp(coeff.) | exp(s.e.) | exp(−coeff.) | coeff. | s.e. | exp(coeff.) | |||
Geographic region () | ||||||||
East Swiss Plateau (GE) | Baseline | Baseline | ||||||
West Swiss Plateau (GW) | 0.881 | |||||||
Alps and Prealps (GA) | 0.870 | |||||||
Romandy (GR) | . | 1.082 | ||||||
Italian-speaking area (GI) | 1.345 | |||||||
Outside Switzerland (OT) | 0.851 | . | ||||||
Number of contracts () | ||||||||
1 | Baseline | |||||||
2 | 0.111 | |||||||
3 | 0.074 | |||||||
0.063 | ||||||||
Access channel () | ||||||||
Tied agent (TA) | Baseline | Baseline | ||||||
Independent intermediary (IY) | 1.080 | |||||||
Broker (BR) | 1.765 | |||||||
Internet/insurer’s website (IT) | 1.029 | |||||||
Other (OT) | 3.040 | |||||||
Age (, in years) | ||||||||
18–19 | 0.209 | |||||||
20–21 | 0.280 | |||||||
22–23 | 0.388 | |||||||
24–25 | 0.624 | |||||||
26–28 | 0.872 | |||||||
29–59 | Baseline | Baseline | ||||||
0.847 | ||||||||
CA contract premium (, in CHF) | ||||||||
18–473 | 1.327 | |||||||
474–1676 | Baseline | Baseline | ||||||
1677–2161 | 1.413 | |||||||
2.327 | ||||||||
Distribution | Exponential | Weibull | Gamma | Log-Normal |
---|---|---|---|---|
CA cohort | 108,385 | 106,309 | 106,332 | 106,306 |
HL cohort | 111,327 | 107,822 | 107,867 | 107,652 |
Cox Model (8) | AFT Model (9) | |||||||
---|---|---|---|---|---|---|---|---|
exp(coeff.) | exp(s.e.) | exp(−coeff.) | coeff. | s.e. | exp(coeff.) | |||
Urbanicity () | ||||||||
Urban (UU) | Baseline | Baseline | ||||||
Rural (UR) | ||||||||
Number of contracts () | ||||||||
1 | Baseline | |||||||
2 | ||||||||
3 | ||||||||
Access channel () | ||||||||
Tied agent (TA) | Baseline | Baseline | ||||||
Independent intermediary (IY) | ||||||||
Broker (BR) | ||||||||
Internet/insurer’s website (IT) | ||||||||
Other (OT) | ||||||||
Age (, in years) | ||||||||
18–21 | ||||||||
22–25 | ||||||||
26–69 | Baseline | Baseline | ||||||
HL contract premium (, in CHF) | ||||||||
20–80 | ||||||||
81–148 | ||||||||
149–359 | Baseline | Baseline | ||||||
360–578 | ||||||||
579–698 | ||||||||
699–910 | ||||||||
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Staudt, Y.; Wagner, J. Factors Driving Duration to Cross-Selling in Non-Life Insurance: New Empirical Evidence from Switzerland. Risks 2022, 10, 187. https://doi.org/10.3390/risks10100187
Staudt Y, Wagner J. Factors Driving Duration to Cross-Selling in Non-Life Insurance: New Empirical Evidence from Switzerland. Risks. 2022; 10(10):187. https://doi.org/10.3390/risks10100187
Chicago/Turabian StyleStaudt, Yves, and Joël Wagner. 2022. "Factors Driving Duration to Cross-Selling in Non-Life Insurance: New Empirical Evidence from Switzerland" Risks 10, no. 10: 187. https://doi.org/10.3390/risks10100187
APA StyleStaudt, Y., & Wagner, J. (2022). Factors Driving Duration to Cross-Selling in Non-Life Insurance: New Empirical Evidence from Switzerland. Risks, 10(10), 187. https://doi.org/10.3390/risks10100187