Principles of actuarial modelling Flashcards
Model
An representation of a real world system or process
System
A group of interacting, interrelated, or interdependent elements forming a complex whole
Why model?
Control over experimental conditions
Cost Saving (Financial & Time)
Improve understanding
Assist is decision making
Advantage of stochastic models
Advantages of stochastic models
Allows you to make a probabilistic statement - distribution of outputs
Examples of where stochastic models are used?
Capital requirements
Pricing options
Pricing guarantees
How is the complexity of models determined
By the complexity of the relationship between the various model parameters
Key steps in the modelling process
- 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
Advantages of models
- 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
Disadvantages of models
- 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
Stochastic model
- 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
Deterministic model
- 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
When should a deterministic model be used
When one is interested in the results of a single scenario
When should a stochastic model be used
When one is interested in the distribution of results of possible scenarios
State of a model
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)
Discrete states
The variable exhibits step function changes in time
Continuous states
The variables change continuously with respect to time (Eg real time changes in the value of investments)
The decision the use a discrete or continuous state model
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
Scenario based model
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
Proxy models
- 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
What should be considered when assessing the suitability of a model for a particular exercise
- 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
Why may the stability of the relationships incorporated in the models not be realistic in the longer term
Models ignore “higher order” relationships which are of little importance in the short term, but which may accumulate in the long term
Why should actuaries exercise great care and judgement when analysing the output of a model
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
Turing test
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
Sensitivity testing
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
