OPTIMISATION IN CREDIT WHERE CAN OPTIMISATION HELP YOU MAKE BETTER DECISIONS

AND BOOST PROFITABILITY

CSCC XIII

Martin Benson

Jaywing

Many business problems that arise in credit

management can be tackled through

constrained optimisation

“How can I assign loan prices to applications in a way that maximises

profitability, but subject to meeting targets for lending and losses and

being compliant with advertising regulation?”

“How can I assign customers to collections strategies in a way that

maximises cash collected but subject to operational constraints?”

Strategy

Optimisation

Scenario

Decision Units Offers / Actions

Constraints Objective

Assignment

Optimisation

Algorithm

General Decision Optimisation

Strategy

Optimisation

Scenario

Loan

Applications Loan APR

Hit Lending Targets

Don’t Breach Risk Appetite

>50% Loans at Typical APR

Objective

Assignment

Strategy

Design

Loan Pricing

Strategy

Optimisation

Scenario

Credit Card

Accounts

Limit Increase

Amount

Control Incremental Risk

Manage Attrition Levels

Maximise

Profitability

Assignment

Strategy

Design

Credit Card Limit Strategy

Strategy

Optimisation

Scenario

Customers Due

To Roll Off

Discount Period

Retention Offer

Hit Retention Target

Control Risk

Manage Margins

Maximise

Profitability

Assignment

Strategy

Design

Pro-active Retention (Mortgages & CCs)

Strategy

Optimisation

Scenario

Collections

Entrants

Contact

Strategy

Minimum/Maximum Daily

Call Volumes

Hit Target Cure Rates

Maximise Cash

Collected

Assignment

Strategy

Design

Collections Entry Streaming

Benefits of optimisation

Optimisation is proven

to return higher portfolio

profitability than more traditional

techniques, across a range of

industries and use cases. It is

the current state-of-the art in

strategy design. Traditional Approach

Optimised Strategy: Up to 20% uplift

SOLVING OPTIMISATION

PROBLEMS

The Maths of Optimisation

max𝑜∈𝑂𝑓 𝑜

Subject to

𝑐𝑖 𝑜 ≥ 𝑣𝑖 𝑖 = 1, …

Maximise

some function

over all possible parameter values

subject to a set of constraints

Solving is difficult in general

max𝑜∈𝑂𝑓 𝑜

Subject to

𝑐𝑘 𝑜 ≥ 𝑣𝑘 (𝑘 = 1,… )

• General solution techniques exist:

Gradient methods

Nelder-Mead algorithm

Genetic algorithms, etc.

• But, they converge to local maxima, not global

maximum (if they converge at all).

Global Maximum

Local Maxima

𝑓 𝑥

𝑥

Tractable formulation of decision problems

max𝑜𝑖,𝑗 ∈ 0,1

𝐼×𝐽 𝑜𝑖,𝑗𝑓𝑖,𝑗𝑖∈𝐼𝑗∈𝐽

Subject to

𝑜𝑖,𝑗𝑐𝑖,𝑗,𝑘𝑖∈𝐼𝑗∈𝐽

(𝑘 = 1,…)

For each decision unit (enumerated

by I), should you make a particular

offer (enumerated by J): yes=1 no=0

The optimisation goal is a sum of

contribution values, each

corresponding to assignment of an

offer to a decision unit

Also, assume that all constraints are

linear in 𝑜𝑖,𝑗

Tractable but not trivial!

max𝑜𝑖,𝑗 ∈ 0,1

𝐼×𝐽 𝑜𝑖,𝑗𝑓𝑖,𝑗𝑖∈𝐼𝑗∈𝐽

Subject to

𝑜𝑖,𝑗𝑐𝑖,𝑗,𝑘𝑖∈𝐼𝑗∈𝐽

(𝑘 = 1,…)

• Binary Integer Program - convergence to

global optimum is

guaranteed...eventually

• Still difficult - BIPs are NP-complete

• Most statistical software packages can

solve BIPs using generic algorithms, but

may take a very long time, even for

small problems

• However, use of proprietary heuristic

algorithms can enable even large

problems to be solved quickly

PREDICTIVE MODELS

Objective

Modelling requirement

• A key requirement for optimisation is

the ability to predict objective values for

every decision unit, for every offer

Offers Decision

Units

• Could attempt to model the

relationship directly…

• …but it’s not a good idea! Too many

moving parts in the middle. Instead…

Model?

Strategy

Optimisation

Scenario

Loan

Applications Loan APR

Hit Lending Targets

Don’t Breach Risk Appetite

>50% Loans at Typical APR

Objective

Assignment

Strategy

Design

Loan Pricing example

Expected

Profit

Interest Revenue

Expected Loss

Cost of Capital

Fee Income

Other Costs

Prob. of

Take Up

PD

EAD, LGD

Voluntary Attrition

APR

Offered

Customer

Profile

Fee Amounts

Loan Amount/Term

Cost Information

Profit Per

Loan

Profitability map

Expected

Profit

Interest Revenue

Expected Loss

Cost of Capital

Fee Income

Other Costs

Prob. of

Take Up

PD

Voluntary Attrition

APR

Offered

Customer

Profile

Fee Amounts

Loan Amount/Term

Cost Information

Profit Per

Loan

EAD, LGD

Offers Decision Units Objective

Regression Model Parameter Derived

…create errors in objective estimates …generate sub-optimal decisions

Model errors drive decision errors

0%10%20%30%40%50%60%70%80%90%

100%5

.9%

6.9

%

7.9

%

8.9

%

9.9

%

10.9

%

11.9

%

12.9

%

13.9

%

14.9

%

Pro

bab

ilit

y o

f Take

-up

APR

Actual TU Rate

TU Model 1

TU Model 2

5.9

%

6.9

%

7.9

%

8.9

%

9.9

%

10.9

%

11.9

%

12.9

%

13.9

%

14.9

%

Exp

ecte

d P

rofi

t APR

TU Model 1

TU Model 2

Errors in predictive models…

Historic strategy can create modelling challenges

Historic strategy may confound data…

Ris

k B

an

d 1

Ris

k B

an

d 2

Ris

k B

an

d 3

Ris

k B

an

d 4

Ris

k B

an

d 5

…Masking true offer impacts

0%10%20%30%40%50%60%70%80%90%

100%

5.9

%

6.9

%

7.9

%

8.9

%

9.9

%

10.9

%

11.9

%

12.9

%

13.9

%

14.9

%

Pro

bab

ilit

y o

f Take

-up

APR

0%10%20%30%40%50%60%70%80%90%

100%5

.9%

6.9

%

7.9

%

8.9

%

9.9

%

10.9

%

11.9

%

12.9

%

13.9

%

14.9

%

Pro

bab

ilit

y o

f Take

-up

APR

Extrapolation potentially drives under-performance

0%10%20%30%40%50%60%70%80%90%

100%5

.9%

6.9

%

7.9

%

8.9

%

9.9

%

10.9

%

11.9

%

12.9

%

13.9

%

14.9

%

Pro

bab

ilit

y o

f Take

-up

APR

Extrapolation Over/under prediction of propensities

Overestimation of the value of some offers

Selection of suboptimal offers

Strategy under delivers, models look misaligned

How to prevent problems

Constrain optimisation

only to allow offers that

are ‘similar’ to previous

experience

Introduce small

randomised control

groups to support

future modelling

Updated strategy and

testing generates

richer data

Build models on the

data that are

available

Iterate to unlock the full potential of optimisation in a controlled manner

SUMMARY

Summary

• Many business problems encountered in credit management can be addressed through the

use of optimisation techniques

• Optimisation can deliver significant benefits over traditional approaches to strategy design.

• However, this is not straightforward, and success requires the right expertise and tools

• Careful consideration must be given to what models are required to support optimisation, and

special care taken to ensure that areas of model weaknesses cannot compromise strategy

performance

Interested in finding out more?

Read our White Paper:

www.jaywing.com/creditriskoptimisation/