Principles of actuarial modelling

Question 1

Model

Answer 1

An representation of a real world system or process

Question 2

System

Answer 2

A group of interacting, interrelated, or interdependent elements forming a complex whole

Question 3

Why model?

Answer 3

Control over experimental conditions

Cost Saving (Financial & Time)

Improve understanding

Assist is decision making

Advantage of stochastic models

Question 4

Advantages of stochastic models

Answer 4

Allows you to make a probabilistic statement - distribution of outputs

Question 5

Examples of where stochastic models are used?

Answer 5

Capital requirements
Pricing options
Pricing guarantees

Question 6

How is the complexity of models determined

Answer 6

By the complexity of the relationship between the various model parameters

Question 7

Key steps in the modelling process

Answer 7

• Develop a well-defined set of objective that need to be met by the modelling process
• Plan the modelling process and how the model will be validated
• Collect and analyse the necessary data for the model
• Define the parameters for the model and consider appropriate parameter values
• Define the model initially by by capturing the essence of the real-world system
• Involve experts of the real-world system to get feedback on the validity of the conceptual model
• Decide on whether a simulation package or a general-purpose language is appropriate for the implementation of the model
• Write the computer program for the model
• Debug the program to make sure it performs the intended operations in the model definition
• Test the reasonableness of the output of the model
• Review and carefully consider the appropriateness of the model in light of small changes in the input parameters
• Analyse the output of the model
• Ensure any professional guidance has been complied with
• Communicate and document the results of the model

Question 8

Advantages of models

Answer 8

• Systems with long time frames can be studies in compressed time
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• Different future policies or possible actions can be compared to determine which best suits the requirements or constraints of a user
• In a model of a complex system we can usually get control over the experimental conditions and reduce the variance of the results output from the model without upsetting their mean values

Question 9

Disadvantages of models

Answer 9

• Model development requires a considerable investment of time and expertise
• In a stochastic model, for any set of input only gives estimates of a model’s outputs so several independent runs are needed for each set of inputs
• Models are more useful for comparing the results of input variations than for optimising outputs
• Models rely heavily on the data input and if the data quality is poor or lacks credibility the models is also likely to be flawed
• The users of the model needs the understand the uses to which it can be safely put as an model can be inappropriate for certain uses
• It is not possible to include all future events in a model
• It may be difficult to interpret some of the outputs of the model (Eg. the model may only be valid in relative terms rather than absolute terms - an investment may be less risky than another, but still very risky)
• One can be lulled into a false set of confidence if a model give impressive outputs, but it still needs to pass the tests of validity and verification

Question 10

Stochastic model

Answer 10

• A model that that recognises the random nature of the input components
• The output is random in nature - like the input which are random variables
• The output is only an estimate of the characteristics of the model for a given set of inputs
• Several independent runs are required for each sets of inputs so that statistical theory can be used to help in the study of the implications of the set of inputs

Question 11

Deterministic model

Answer 11

• A model that does not contain any random component

- The output is determined once the set of fixed inputs and the relationship between them has been defined

Question 12

When should a deterministic model be used

Answer 12

When one is interested in the results of a single scenario

Question 13

When should a stochastic model be used

Answer 13

When one is interested in the distribution of results of possible scenarios

Question 14

State of a model

Answer 14

The set of variables that describe the system at a particular point in time taking into account the goals of the study (eg. healthy, sick, dead)

Question 15

Discrete states

Answer 15

The variable exhibits step function changes in time

Question 16

Continuous states

Answer 16

The variables change continuously with respect to time (Eg real time changes in the value of investments)

Question 17

The decision the use a discrete or continuous state model

Answer 17

Determined by the objective of the study rather than whether or not the system itself is of a discrete or continuous nature

For a monte carlo simulation one as to discrete the time step. The higher the precision the time step, the longer the simulation will run

Question 18

Scenario based model

Answer 18

Takes into consideration a particular scenario; that is a series of input parameters based on the scenario

Different scenarios would be useful in decision analysis as one can evaluate the expected impact of a course of action

Question 19

Proxy models

Answer 19

• Used to replace monte carlo simulations
• Expected to be faster but less accurate

A simplified formula is developed that we believe predicts the result with reasonable accuracy, and this is then used as a substitute for running the full model

Question 20

What should be considered when assessing the suitability of a model for a particular exercise

Answer 20

• The objective of the modelling exercise
• The validity of the model for the purpose to which it is to be put
• The validity of the data to be used
• The validity of the assumptions
• The credibility of the data input
• The credibility of the results output
• The current relevance of models written and used in the past
• The impact of correlations between the random variables that drive the model
• The extent of correlations between the various results produced from the model
• The ease with which the model and its results can be communicated
• Regulatory requirements

Question 21

Why may the stability of the relationships incorporated in the models not be realistic in the longer term

Answer 21

Models ignore “higher order” relationships which are of little importance in the short term, but which may accumulate in the long term

Question 22

Why should actuaries exercise great care and judgement when analysing the output of a model

Answer 22

The observations in the process are correlated with each other and the distributions of successive operations change over time

The fatally attractive temptation of assuming that the observations are independent and identically distributed is to be avoided

Question 23

Turing test

Answer 23

Experts on the real world system are asked to compare several sets of real-world and model data without being told which are which

If these experts can differentiate between the real-world and model data, their techniques in doing so could be used to improve the model

Question 24

Sensitivity testing

Answer 24

Test the reasonableness of the output of the model against the real world

An examination of the sensitivity of the outputs to small changes in the inputs or their statistical distributions should be carried out

The appropriateness of the model should then be reviewed, particularly if small changes in inputs or their statistical distributions give rise to large changes in the outputs

This determines the key inputs and relationships to which particular attention should be given in designing and using the model

Question 25

Why is the communication and documentation of the results important

Answer 25

The client has to accept the model as being valid and a useful tool in decision making

The communication has to take into account the knowledge of the target audience and their viewpoint

It is important to ensure that any limitations on the use and validity of the model are fully appreciated