Chapter 1: Actuarial modelling

Question 1

Why do we use models

Answer 1

We use models because it might be
* Too risky
* Too expensive
* Too slow
To test a proposed change in the real world even on a sample basis

The effect of changing parameter values can be investigated before implementation

Question 2

Explain the core pillars of building a model

Answer 2

Data is collected, and judgement needs to be made about its relevance (especially to the future environment) and quality. Data might result from:
* Past observations
* Current observations
* Future expectations

The objectives of the modelling exercise have to be clearly defined and considered when choosing the model and model parameters.

Question 3

Outline the steps in building a model

Answer 3

1. Develop a set of well-defined objectives that need to be met by the modelling process.
2. Plan the modelling process and how the model will be validated - diagnostic tests to make sure that the model is meeting the objectives.
3. Collect and analyse the necessary data for the model.
4. Define the parameters for the model and consider appropriate parameter values.
5. Define the model initially by capturing the essence of the real-world system.
6. Involve experts in the real world system you are trying to imitate to get feedback on the validity of the conceptual model.
7. Decide on either a simulation package or a general purpose language for implementation. Choose a statistically reliable random number generator that will perform adequately in the context of the complexity of the model.
   a. Recall that the generator could be assuming a normal, uniform, etc. so this choice should be suitable for your model.
8. Write the computer program for the model.
9. Debug the program to make sure it performs the intended operations in the model definition.
10. Test the reasonableness of the output from the model.
11. Review and carefully consider the appropriateness of the model in light of small changes in input parameters.
12. Analyse the output from the model.
13. Ensure that any relevant professional guidance has been adhered to.
14. Communicate and document the results and the model.

Question 4

Benefits of modelling

Answer 4

• Systems will long time frames can be studied in compressed time.
• Simulation can assist with modelling complex systems with stochastic elements, which cannot be properly described by a logical or mathematical model whose results are eas;y to interpret.
• Different future policies or possible actions can be compared to see which results best suit the constraints of the user.
• We get control over experimental conditions so we can reduce the variance without significantly impacting the mean of the results.

Question 5

Drawbacks of modelling

Answer 5

• Need considerable investment of time and expertise to:
• Check assumptions
• Check the code
• Check reasonability of the results
• Interpretation of the results by others.
• Computing power: In a stochastic model, for any given sets of inputs each run gives only estimates of a model’s outputs. So, to study the outputs for any given sets of inputs, several independent runs of the model are needed.
• As a rule, modells are more useful for analyse the output of different input variations rather than giving the sets of inputs for a desired outcome.
• Models may look impressive when run of a computer, which may lead to the danger of a false sense of confidence. If a model has not passed validity tests, its impressive outputs are a poor substitute for its inability to imitate the real world system.
• Models rely heavily on data input, so if its quality is poor, then the output will be poor.
• It is important that users are aware of the uses that a model may be put to, otherwise there is a risk of a model being used as a black box, from which all outputs are considered as valid without considering the models appropriateness for the situation at hand.
• It is not possible to include all future events of a model.
• It may be difficult to interpret some model outputs.

Question 6

Describe the characteristics, and explain the use of, scenario-based proxy models.

Answer 6

• A scenario based model is one that takes into consideration a particular scenario, that is a set of parameters based on this specific scenario.
• A proxy model may be used to replace Monte Carlo simulations which is expected to be faster but less accurate.
• This is done by developing a simplified formula based on the same set of assumptions, this is then ran instead of the full model.

Question 7

Describe, in general terms, how to decide whether a model is suitable for any particular application.

Answer 7

• Credibility: of data and results
• Objectives
• Correlations: impact of input RV and extent of correlation of results
• O
• Communication
• Relevance: current and past data
• Accuracy
• Validity: data, purpose and assumptions
• Eerros: model or parameters
• Regulatory requirements

Question 8

Explain the difference between the short-run and long-run properties of a model, and how this may be relevant in deciding whether a model is suitable for any particular application.

Answer 8

• Models are simplified versions of the real world, they might ignore higher order relationships that are not significant in the short-term, but may accumulate in the long term. .
• Therefore the stability of the relationship established in the model may not be realistic in the longer term.

Question 9

Describe in general terms, how to analyse the potential output from a model, and explain why this is relevant to the choice of model

Answer 9

• Can be done using a Turing test, where experts are asked to compare sets of real world and model data without being told which one is which. If the experts can differentiate between them, the techniques for doing so may be used to improve the model
• If small changes in the input of a model gives rise to large changes, then our initial choices are crucial including the model and its parameters.

Question 10

Explain the difference between a stochastic and deterministic model, and identify the advantages/disadvantages of each.

Answer 10

• A model that recognises the randomness of model inputs.
• The output is only an estimate of the characteristics of a model given a set of inputs.
• Several independent runs are needed for each set of inputs so that statistical theory can be used to help study the implications of the set of outputs.
  Deterministic model:
• A model that does not contain any random component
• Output is determined once a fixed set of inputs have been determined and the relationship between then defined.
• Choosing between the two depends on whether one wants the results of a scenario or a distribution of possible scenarios.
• If a stochastic model is investigaated using Monte Carlo simulations, then this provides a collection of suitably large number of deterministic models, each considered equally likely.
• Sometimes a stochastic model’s results can be determined using analytical methods, these are preferred to Monte Carlo simulations as they are faster and less resource intensive.