Deep learning applications: policyholder behavior modeling and beyond

# Deep learning applications: policyholder behavior modeling and beyond
## <a href='https://kevinykuo.com/talk/2018/10/soa-annual/'>kevinykuo.com/talk/2018/10/soa-annual</a> #SOAannual
### Bob Crompton, Frankie Logan, Kevin Kuo
### October 2018

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# Introduction

Your hosts and their drinks of choice (at the moment).

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# The actual content...

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# Deep Learning - What is it?

.Large[.Center[A statistical technique for classifying patterns, based on sample data, using neural networks with multiple layers]]

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# Obligatory Deep Learning Illustration

![](img/gen_nn.png)

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# Historical Perspectives

.Large[

* Neural networks have been around for decades (Perceptron algorithm dates to 1957)

* Increase in computer power & improvement in Big Data algorithms have made multiple-layer neural networks feasible

* 2012 was a break-through year for Deep Learning due to success on the Imagenet Challenge

]

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# Deep Learning - Strengths

.Large[

* Can represent an finite mapping between input & output provided there is infinite data

* In practice, large data sets often provide good results
  * How large is "large?"
  
    * Krizhevshy et al's Imagenet model had the following attributes
    
      * 1 million distinct examples
      * 9 layers
      * 650,000 nodes
      * 60 million parameters
]
      
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# Deep Learning - Strengths (Continued...)

.Large[

* Deep learning does well at these tasks:
  * Object recognition
  * Speech recognition
  * Other non-linear "natural" data
  * Game play

* Clever mapping of outputs to inputs increases applicability of this approach
]
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# Deep Learning - Limitations

.Large[

* Data hungry
  * Infinite data not available

* Limited capacity for analogies

* Generalization possible only when differences between training data and test data are small

* Lack of transparency

* Lack of hierarchical recognition

]
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# Deep Learning - Current Insurance Applications

.Large[

* Data on General AI & Machine Learning in Insurance is extensive
* Data on Deep Learning in particular is not widespread, but there do seem to be a few uses

* Property claims
  * Claims Fraud
  * Investment analysis

]
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# Deep Learning - Potential Applications

.Large[

* M&A Analysis

* Natural language processing & report writing
]

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# The real reason we care about deep learning...

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![](img/doge1.png)

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# Slightly more technical...

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# Learning

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# Learning

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# Learning

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# Case study time!

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# Term Life Insurance 
.large[
- Insurance companies provide coverages for a set number of years or "term" (e.g. 15 years) with a fixed premium rate.  After the term is over, the insured has a choice of lapsing or continuing the coverage with a different (usually higher) premium rate.

- Shock Lapse - the high lapse rate phenomenon after post level premium term
 
  * Mortality implication - the policyholders that continue the coverage usually "need" it.

* Profitability - in addition to higher mortality rate, insurers are receiving less premium.
]
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#To improve risk management & better retain policyholders, we need to understand which group of policyholders will most likely to experience shock lapse.

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# Current Study

.Large[
- SOA has conducted studies to predict lapse rate using regression models (e.g. generalized linear model aka "GLM")

- A few takeaways:

- Higher face amount -> higher lapse rate
  
  - Higher Premium Jump % -> higher lapse rate
  
  - Older issue age -> lapse rate increases at a decreasing rate

SOA 2014 Post Level Term Lapse & Mortality Report: https://www.soa.org/experience-studies/2014/research-2014-post-level-shock/
]
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# Data

.Large[
* Companies that participated in the SOA study provided a list of inforce and terminated level term policy with the exact issue dates and dates of termination respectively.

* Each cell, or row, represents a policy block.

* A grace period adjustment was made to moved shock lapses that were reported 30 to 100 days into the first duration of the post-level period back to the final duration of the level period. 
]

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# Data (Cont.)

Let's take a look at our data

```
## Observations: 345,627
## Variables: 15
## $ lapse_study_year <chr> "2000-2001", "2008-2009", "2000-2...
## $ duration <chr> "6-9", "10", "6-9", "6-9", "6-9",...
## $ gender <chr> "M", "F", "F", "M", "F", "F", "M"...
## $ issue_year <chr> "1994-1996", "1997-1999", "1994-1...
## $ issue_age <chr> "50-59", "40-49", "40-49", "40-49...
## $ face_amount <chr> "A. < 100k", "B. 100k-249k", "C...
## $ post_level_premium_structure <chr> "1. Premium Jump to ART", "1. Pre...
## $ premium_jump_ratio <chr> "Y. Unknown", "Y. Unknown", "Y. U...
## $ risk_class <chr> "Agg/Unknown", "Super-Pref NS", "...
## $ premium_mode <chr> "2. Semiannual", "4. Monthly", "3...
## $ exposure_amount <dbl> 325000, 1232000, 2600000, 1550000...
## $ exposure_count <dbl> 7.0000, 11.0000, 7.0000, 4.0000, ...
## $ lapse_amount <dbl> 25000, 500000, 0, 1250000, 0, 377...
## $ lapse_count <dbl> 1, 5, 0, 3, 0, 11, 6, 3, 0, 0, 0,...
## $ policy_year <int> 2000, 2008, 2000, 2008, 2003, 201...
```

Source: [SOA 2014 Post Level Term Lapse & Mortality Report](https://www.soa.org/experience-studies/2014/research-2014-post-level-shock/)
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#Predictors and Response

Predictors:

```
## [1] "Gender"                       "Issue Age"                   
## [3] "Face Amount"                  "Post Level Premium Structure"
## [5] "Premium Jump Ratio"           "Risk Class"                  
## [7] "Premium Mode"
```

Responses:

```
## [1] "Lapse Count Rate"
```

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# Data Prep

1. Filter records for the 10th policy duration

2. Filter records for positive exposure count and amount

3. Create lapse count rate and lapse amount rate variables

Training set: policy year < 2010

Validation set: policy year = 2010

Testing set: policy year > 2010

- In an **ideal world**, the lag between training and validation should be much **longer**. Our goal is to predict lapse rate at policy inception.

--

No more feature engineering! Let's get to modeling.
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# Models

.Large[
- Historical Average - baseline

- Generalized Linear Model (GLM) - technique from SOA study

- Gradient Boosting Machine (GBM)

- Neural Net

]
--

.Large[
Evaluation Metric:

- RMSE (Root Mean Squared Error)

- R2 (R-Squared)

- MAE (Mean Absolute Error)

]
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# Baseline, Regression & Machine Learning Models

|Metric | Historical Average | GLM | GBM |
|-------------| :--------------------:| -----:| -----:|
|RMSE |0.298 |0.273 |0.272 |
|R2|0.283 |0.333 |0.339 |
|MAE |0.184 |0.197 |0.191 |

<big>As you can see, the model tends to get better as we progress from simple averages to machine learning models!</big>

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# Neural Net

.Large[

* Since neural net is a matherical model, all inputs must be a number. Before we can build our model, we have to convert our categorical predictors to numerical predictors.

* Ways to convert categorical variable to numeric variable:

* Assign nominal or ordinal number

* One-hot encoding
 
 * Embedding

]

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# One-Hot Encoding

One-Hot Encoding - Fancy phrase for _dummy variable_?

```
##   gender
## 1   Male
## 2 Female
## 3 Female
## 4   Male
```

```
##   Male Female
## 1    1      0
## 2    0      1
## 3    0      1
## 4    1      0
```
]

--
.pull-right[

* More values in the predictor -> higher dimenisons.

* One-hot encoding has a few disadvantages:
  
  * it doesn't look at relationships between the different values of the predictor
  
  * it is computationally expensive

]
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#Embedding Layers

* In embedding, we map each of the categorical variable to an embedding space. Within this space, values with similar output are mapped close together.

Example:

```
Risk Class

[1] "Super-Pref NS" "Agg/Unknown"   "Non-Pref NS"   "Pref SM"       "Pref Best NS"  "Undiff SM"    
[7] "Pref Resid NS" "Undiff NS"     "Non-Pref SM"

```

* Instead of creating an additional variable for each of the levels in risk class, we can map it into a multi-dimensional embedding space.

* Embedding allow us to:

* learn about the intrinsic properties of variable.

* reduces resource cost
  
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#Embedding Layers - Risk Class

("Super-Pref NS" is more closely related to "Pref Resid NS" than "Pref SM")
]

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# Neural Net Structure

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# Neural Net Result

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# Model Comparison

|Metric | Historical Average | GLM | GBM | Neural Net|
|------------ |:---------------------:| -----:| -----:| ------------------------------------:|
|RMSE |0.298 |0.273 |0.272 |0.266 |
|R2|0.283 |0.333 |0.339 |0.366 |
|MAE |0.184 |0.197 |0.191 |0.182 |

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# Interpreting the Models

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# Visualizing the premium jump embedding

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# Comparing model performance

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# Comparing model performance

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# Variable importance

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# Variable importance - comparison

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# Prediction breakdown

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# Prediction breakdown - comparison

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# Couple quick words on software...

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# Tools

- [R](https://www.r-project.org/) 
  * Data Prep - [`tidyverse`](https://www.tidyverse.org/), [`recipes`](https://github.com/tidymodels/recipes)
  
  * Modeling - [`keras`](https://keras.rstudio.com/), [`xgboost`](https://xgboost.readthedocs.io/en/latest/)
  
  * Model Evaluation/Visualization - [`yardstick`](https://github.com/tidymodels/yardstick), [`DALEX`](https://github.com/pbiecek/DALEX/tree/master/R), [`deepviz`](https://github.com/andrie/deepviz)

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# Deep learning libraries

- PyTorch ([https://pytorch.org/](https://pytorch.org/))
  - Supported by Facebook.
- TensorFlow ([https://www.tensorflow.org/](https://www.tensorflow.org/)) + Keras ([https://keras.io/](https://keras.io/))
  - Supported by Google. R interface supported by RStudio.
]

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# Q & A

.large[
- Link to slides/code: [https://kevinykuo.com/talk/2018/10/soa-annual](https://kevinykuo.com/talk/2018/10/soa-annual)

- GitHub repo: [github.com/kevinykuo/shocklapsedemo](https://github.com/kevinykuo/shocklapsedemo)

- If you care about P&C loss reserving (GI Trac~~t~~k anyone?), check out [DeepTriangle: A Deep Learning Approach to Loss Reserving](https://arxiv.org/abs/1804.09253)
]