© English Matthews Brockman 2000. Business Planning in Personal Lines using DFA A Talk by Mike Brockman and Karl Murphy 2001 Joint GIRO/CAS Conference

© English Matthews Brockman 2000


Business Planning in Personal Lines using DFA

A Talk by Mike Brockman

and Karl Murphy

2001 Joint GIRO/CAS Conference

3 – 6 October 2001, Glasgow


What is DFA?

“A process for analysing the financial condition of an insurance enterprise, by calculating a company’s risk profile through introducing the uncertainties of the real world into the management process”

- investigating risk using simulation


Traditional Approach to Planning

• Looks at point estimates

• Scenario based only

• Tends not to be holistic in nature


Why Use is DFA?

• DFA is a methodology which introduces the uncertainties of the real world into the management process

• DFA recognises the fact that in any given scenario a range of outcomes is possible

• Dynamic in sense of

– Stochastic view of experience

– Dynamic view of strategy


Output From a DFA Model

• Varies with nature of the problem

• For a particular business plan obtain a loss profile

• Need concept of risk (VAR or TVAR?)

• Risk – return measure (e.g. Efficient frontier)

• Optimal strategies based on risk measure


Efficient Frontier Analysis

• Classical efficient frontier techniques can be used

• Definition of risk needs to be determined

• Can assist in deciding business mix

• Every point is a strategy


How to Build a DFA Model:The Basic Building Block

InputOutput

BaseModule

Marginal distributions

Correlation / Dependency

Structure

Deterministic inputs

Simulated output

variables with

dependency structure


Example Underwriting Module

A ttrit io n a l C la im s U n d e rw rit in g cyc le C a t m od u le P rice E la s tic ity R e in su ra n ce

U n d e rw rit in g M o d u le

• Each module does not necessarily have only one output

• Enables accurate modelling of marginal distributions

• Dependencies between modules modelled in the higher module

• List of submodules is not necessarily complete!

• Each module may represent a segment


Business Unit Example

A sse t M od u le R e se rv in g M o d u le U n d e rw rit in g M o d u le P la nn in g M od u le

B u s in ess U n it

• Modular approach enables replacement of modules as and when necessary

• All variables from within a module/sub-module may be made available to model dependency structures


High Level Models

C o m m e rc ia l L in esD F A M o d e l

P e rso n a l L in esD F A M o d e l

O th er B u sin e ss a reaD F A M o d e l

G lo b a l D F A M o d e l


Business Considerationsin Model Design• Business Volumes

- Expenses- Operational infrastructure- Solvency and capital requirements

• Premium Income Levels- Competition- Insurance cycle- Pricing strategy- Business volume

• Extreme Events- Impacts losses- Operational infrastructure- Impacts prices


Business Considerationsin Model Design

• Lines of Business- Behave differently

- Different cycles

- Different returns

- Different risks

• Economic Factors- State of the economy

- Inflation

- Interest Rates

- Stock Market

- Litigiousness


Financial Managementof your Business

• How do you decide which line of business to grow?

• How to you determine the optimal pricing strategy?

• How do you measure which strategy is best?

• How do you allow for uncertainty?

• How do you allow for correlations and dependencies?


The Insurance Cycle Building Block


Can the Cycle Be Predicted?

• Lines of business behave differently

• Competition and consolidation

• Information

• Technology

• Barriers to entry


Lo

ss R

atio

Underwriting Cycle by Class

Property

.4

.6

.8

1

1.2

Motor

Liability

86 88 90 92 94 96 98

.4

.6

.8

1

1.2

Acc/Health

86 88 90 92 94 96 98


Loss

Rat

io

Motor Loss Ratios by Year

Observed Loss Ratio Sin-Cos AR(2)

1985 1987 1989 1991 1993 1995 1997 1999 2001

.5

.6

.7

.8

.9

1


Can the Cycle Be Predicted?

• Possibly over short term but uncertain

• Some lines more stable

• Impact of extreme events

• A range of future scenarios

• Could assign probabilities to scenarios


Building a Model to Manage Uncertainty

A Simple Example

• How does your future view of the cycle affect your capital requirements and the probability of ruin?

• How do you choose which line of business to grow?


Model Assumptions

• 2 classes: Motor and Property

• 1000 policies in each class initially

• Initial ave loss £1200 for Motor, £1800 for Property

• Claims frequency 20% for Motor, 15% for Property

• Ave loss ratio 99% for Motor, 98% for Property

• Property more volatile


Model Assumptions

• Initial premium approx £500,000 split ~ 50:50 motor/household

• Initial Capital £1,000,000

• Capitalised such that if growth is 5% per annum, theBoard is happy with the level of risk

• Company follows premium levels set by the market

• Assume the company can meet its growth targets

• Simulate over two complete cycles





Results from Different Growth Scenarios

Motor Growth

Property Growth

Extra Expected

Profit

Extra* Capital

Required5% 5%10% 10% 35% £0.4m20% 0% 0% £0.5m0% 20% 50% £1.5m

* to maintain risk level


Business Planning Model

Documents

© English Matthews Brockman 2000. Business Planning in Personal Lines using DFA A Talk by Mike Brockman and Karl Murphy 2001 Joint GIRO/CAS Conference