Machine Learning and the Future of the Actuary · The weaknesses of the Solvency II standard...

Machine Learning

the Future of the Actuary

Frank Cuypers

Scenario

Solvency II initiates

New players flood the market with “digital” alternatives to insurance

Insurance industry flood the market with “Fickle Superannuations” with little Solvency II capital

requirements

30% of the insurance players file for bankruptcy

The weaknesses of the Solvency II standard formula become obvious

Who should have known? Who should have warned?

The actuarial profession is discredited

The last Presidents of the SAA, DAV and IFO are burnt at the stake

Scenario

Scenarios

actuaries

tolerated

actuarial

profession

disappears

Actuaries

actuaries

bring value

Whom Shall we Still Need in 2035?

Specialized jobs

Drivers?

Nurses?

Information intensive jobs

Translators?

Lawyers?

Physicians?

Creative jobs

Architects?

Scientists?

The programmers?

How Shall we Live in 2035?

Will our children still learn how to read & write?

Shall we be terminated?

Shall we become bionically enhanced?

Will eventually joint human & machine crowd intelligence supersede artificial intelligence?

What’s Artificial Intelligence?

artificial intelligence machine learning

predictive modelling data analytics

data mining cognitive computing

decision trees

support vector machines

genetic algorithms Bayesian networks …

k-nearest neighbours

neural networks

Ubiquitous Neural Networks

Higgs search

Spam filters

Travelling salesman problems

Medical diagnosis

Voice recognition & generation

Translation deepl.com

Natural languages processing infocodex.com

Gaming

Image & face recognition how-old.net

𝑦𝑁𝑁 = 𝑐0 + 𝑐1ℎ1 + 𝑐2ℎ2 + 𝑐3ℎ3

Neural Networks in a Nutshell

𝑥 𝑦

𝑦𝑜𝑏𝑠 = 𝑓 𝑥 + 𝜀

Training: minimize 𝑦𝑜𝑏𝑠 − 𝑦𝑁𝑁2

ℎ 𝑎1 + 𝑏1𝑥

Neural Networks

bye bye models…

Neural Networks – 2 Hidden Layers

Applications

regression classification

data processing control systems

robotics

-100,000

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1,000,000

1,100,000

1,200,000

500,000

1,000,000

1,500,000

0 500,000 1,000,000 1,500,000

DATA GLM NN

Applications – Supervised Learning

Regression

Output = e.g. size of claim

Each output neuron

gives a number,

which can take any value

Classification

Output = e.g. type of claim

Each output neuron

gives a probability ,

which all add up to 100%

neural network

-1.0 -0.5 0.0 0.5 1.0

linear model

Applications – Unsupervised Learning

Higgs search

Spam filters

Medical diagnosis

Translation deepl.com

Natural languages processing infocodex.com

Gaming

Image & face recognition how-old.net

Ubiquitous Neural Networks and Disrupters

Higgs search

Spam filters

Medical diagnosis

Translation

Natural languages processing

Gaming

Image & face recognition

Insurance?

Actuarial engineering

• Individual claims development

• Pricing

• Alternative to replicating portfolios

• …

Claims

• Regulation of attritional claims

• Fraud detection

• …

Underwriting & customer relations

• Medical underwriting

• Lapse prediction

• Retention programs

• Behavioural advice (telematics, health,…)

• …

Insurance?

• Pricing

• …

Claims

• Fraud detection

• …

Higgs search

Spam filters

Medical diagnosis

Translation

Gaming

Traditional Loss Development

individual claims

2011 2011

in 2012

2011 in

2012 in

2013 in

Aggregate all claims of a given AY into a single aggregate loss

individual claims annual aggregate loss

Develop with

Chain Ladder

Born-Ferg

Cape Cod

Assume

Homogenous portfolio

Stationary portfolio

Individual Claims Development

Use individual claims information

individual claims annual aggregate loss

Use individual claims information cascading DY neural network

500,000

1,000,000

1,500,000

0 500,000 1,000,000 1,500,000

goal DY 2 DY 3 DY 4 DY 5

DY 6 DY 7 DY 10 DY 12

200,000

400,000

600,000

800,000

1,000,000

1,200,000

0 5 10 15 20

570 570 570 783 783 783

Simple Test

2 types of claims

Cascading DY

1 hidden layer

8 neurons

Paids only

out-of-sample

ICD vs ALD

Aggregate Loss Development

Develop with

Chain Ladder

Born-Ferg

Aggregates all claims

of a given AY

into a single aggregate loss

Works either on paid

or incurred losses

Assumes

Homogeneous portfolio

Stationary portfolio

Develop with

DY or AY cascades

Convolutional networks

Considers all individual claims’

features,

including non monetary inputs

Considers simultaneously

payments and reserves

Works with

Heterogeneous portfolios

Dynamic portfolio

DY Cascade vs Chain Ladder

-8,000,000

-6,000,000

-4,000,000

-2,000,000

2,000,000

4,000,000

6,000,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Accident Year

True - NN

True - CL

-120,000,000

-100,000,000

-80,000,000

-60,000,000

-40,000,000

-20,000,000

20,000,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Accident Year

True - NN

True - CL

-160,000,000

-140,000,000

-120,000,000

-100,000,000

-80,000,000

-60,000,000

-40,000,000

-20,000,000

20,000,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Accident Year

True - NN

True - CL

Insurance?

• Pricing

• …

Claims

• Fraud detection

• …

Higgs search

Spam filters

Medical diagnosis

Translation

Gaming

Insurance AI Patents

Neural network for classifying speech and textural data based on agglomerates in a

taxonomy table

System and method for automated establishment of experience ratings and/or risk reserves

Challenges

Architecture

Data pre-processing

Training

Cross validation

Communication

Challenges: Architecture

Monkey & octopus

Can solve similar problems

Have completely different brains (octopus has 9 brains…)

Dyslexic & autistic humans

Have same brain architectures

Have completely different skills

Neural network

? Activation function (sigmoid)

? Penalty function

? Number of layers

? Number of neurons

? Training strategy

? Fully-connected vs convolutional network

Challenges: Data Pre-Processing

Humans are good at catching flying objects

But less if they are myopic

Humans are good at communicating orally

But less if they are hearing-impaired

Neural network

! Pre-process inputs

! Scale outputs

requires a healthy understanding

of the underlying phenomena

Challenges: Training

How do you learn

A poem

A foreign language

A programming language

A mathematical method

Neural network

Minimize penalty function over a high dimensional parameter space

Backpropagation

Very fast (Python, Matlab)

Steepest gradient local minima

Simulated annealing?

Global minimum?

Untested?

Challenges: Cross Validation

Important technical issue

As important as AvE

Challenges: Communication

You ride a car – do you know how

your ABS works?

your airbag triggers?

it will drive on its own?

You implement Chain Ladder – do you understand why

the link factors take these values?

you may apply this method?

Richard Feynman:

Nobody understands Quantum Mechanics!

Produce with neural networks – illustrate with decision trees

Facts & Alternative Facts

Advantages

Respond very fast

… but training can take long

Can generalize

… and may get it wrong

Are robust

… most of them

Are very flexible with regard to inputs

… if well pre-processed

Can update their knowledge continuously

… with reinforced learning

Fallacies

Needs big data

… a few hundred claims suffice

Needs an IBM Watson

… AI is more than «deep learning»

… most is much easier than translating

Why change proven processes?

… because they can be misleading

… because they can be improved

… because others could do it

Let’s implement a blockchain

Food for Thoughts

actuarial

profession

disappears

If PRS can prototype it in Excel,

it’s not quantum field theory!

actuaries

tolerated

actuaries

bring value

again 1995

Actuaries

Statutory reserving

Different models depending on

data availability / quality

line of business / market

processes / products

actuarial judgment

→ 1st moment of a distribution

standard reserving model

Solvency II

actuarial judgment

→ nth moment of a distribution

standard solvency formula

actuarial judgment

… et Carthago delenda est!

Standard Solvency II formula

Analytic linear approximation

𝑆𝐶𝑅 ← 𝜎2 = 𝜌𝑖𝑗𝜎𝑖𝜎𝑗

Probe the tail with 2nd moments

Internal models

Numerical aggregation of realistic distributions

𝑆𝐶𝑅 ← risk1⊗ risk2⊗ risk3⊗⋯

Probe the true tail

… et Carthago delenda est!

Cut along

dotted line

Internal models

Numerical aggregation of realistic distributions

𝑆𝐶𝑅 ← risk1⊗ risk2⊗ risk3⊗⋯

Probe the true tail

Frank Cuypers

+41 (41) 725 32 94

frank.cuypers@prs-zug.com

Lecturer’s Coordinates

The IAA

ASTIN what it is

Focuses on non-life insurance

Bridges the gap between practitioners and academics

with meaningful dialogues and research that:

stimulate academics to explore frontiers that are relevant in practice

catalyze the transfer of SoA techniques from academia to the industry

Creates an environment that promotes continuing professional development

ASTIN what it does

Colloquia

Regional meetings

Webinars

Working parties

ASTIN Bulletin

Training in countries with a developing actuarial profession

Bursaries for young actuaries & researchers from developing economies

Online library of technical and practical documents

Experts helpline (work in progress)

ASTIN Working Parties

Foster applied research in general insurance

Extract more value from the intellectual potential of the ASTIN membership

Topics

Focused and short-lived

Practical and useful

Organisation

Bottom-up initiatives: Champions submit short ToR

ASTIN Board endorses ToR and findings

ASTIN provides funding

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