Principles of actuarial modelling Flashcards
14 Key Steps in a modelling process
Advantages of modelling in actuarial work
Time: Models allow us to investigate the future behavior of a process in compressed time
Control of Experimental Conditions: Models allow control over experimental conditions so that we can reduce the variance of the output without affecting the mean values
Simulation Modelling: Complex systems with stochastic elements cannot be properly described by a mathematical or logical model that is capable of producing results that are easy to interpret. Simulation modelling is a way of studying these complex systems
Comparison: Different future policies or possible actions can be compared to see which best suits the requirements or constraints of the user
Disadvantages
Time and Expertise: Model development requires a considerable investment of time and expertise
Runs: In a stochastic model, for any given set of inputs each run only gives estimates of the output. So to study outputs for any given set of inputs, several independent runs of the model are needed.
Usefulness: Models are useful for comparing results of input variations than optimising outputs
Confidence: Model can look impressive when run on a computer so there is also a danger that one gets lulled into false sense of confidence.
Data: Models rely heavily on the data input. If the data quality is poor or lacks credibility then the output from the model is likely to be flawed.
Blackbox: There is a danger of using a model as a ‘black box’ from which it is assumed that all results are valid (without considering the appropriateness of using the model for the input data and the output is expected. )
Possibility: It is not possible to include all future events in a model
Interpretation: It may be difficult to interpret some of the outputs of the model.They may only be valid in relative rather than absolute terms.
Suitability of a model
OV3 PC3 C2RAE
O: objectives of the modelling exercise
V: validity of the model for the purpose to which it is be put
validity of the data to be used
validity of the assumptions
P: the possible errors associated with the models or parameters used not being a perfect representation of the real-world situation being modelled
C: impact of correlations between the random variables that drive the model
the extent of correlations between the various results produced from the model
current relevance of the models written and used in the past
C: credibility of the data input
credibility of the results output
R: Regualation requirements
A:: dangers of spurious accuracy
E: ease with which the model and its results are can be communicated
Turing Test
experts on the real world system are asked to compare several sets of real world and model data without being told which is which
if an expert can differentiate between the real world and model data their technique for doing could be used to improve the model
What to consider when communicating the results
KVVDL2
Take into consideration the knowlegde and the viewpoint of the target audience.
ensure the client accepts the model as being valid and useful tool in decision making,
ensure that any limitations on the use and validity of the model are fully appreciated
Deterministic vs Stochastic (Randomness and Output and Scenario)
Randomness: A stochastic model is one that recognises the **random nature **of the input components
A model that does not contain any random component is deterministic in nature
Output: In a deterministic, the output is determined once the** set of fixed inputs** and the** relationship** between them is defined.
In a stochastic model, the output are random in nature (like the inputs which are random variables). Output is merely a estimate of the characteristics of the model given the set of inputs
Scenario: A deterministic model will give one the results of the relevant calculations for a single scenario; a stochastic gives **distributions of the relevant results **for a distribution of scenarios
Issues/parameters to consider when modelling a life office
(think about which ones have to do with policyholder and ones have to do with insurer, external) three of each btw
regulations, taxation, cancellation terms, future events affecting returns, inflation, new business, lapses, mortality and expenses
Scenario Based
would take into consideration a particular scenario; that is a series of input parameters based on this scenario. Different scenario would be useful in decision making as one can evaluate the impact of a course of action
Proxy
used to replace monte carlo simulations (used to project assests and liabilities)
Example of when you would use scenario based
we could model the financial performance of a company under different future scenarios such recession or economic boom. The value of any input paramters (inflation,interest rate or level of taxation) would be select to be appropriate to the specific scenario under consideration
Sensitivity analysis/testing
involves testing the robustness of the model by making small changes to the input parameters. This should result in small changes to the output from the model that consistent with the real world behaviour of the situation we are modelling
Advantages of stochastic model over the deterministic
It reflects reality as accurately as possible as it imitates the random nature of the variables involved
can provide information about the distribution of the results, not just a single estimate figure
How are a stochastic model and a deterministic model investigated?
A stochastic model can be investigated using Monte Carlo simulation, which provides a large number of different deterministic models, each of which is equally likely. It can also be investigated using analytical methods which is much quicker than the Monte Carlo.
The results of a deterministic can be obtained by direct calculations or numerical approximations (integrate and solve differential equations)
Stochastic model can be done via analytical approach or monte carlo simulation. Advantage and disadvantage of both
Analytical: (POCCS)
Precision: if a stochastic model is sufficiently tractable, analytical methods will produce more precise results which is preferable
Speed: much quicker than Monte Carlo simulation as One can analyse the effects changes to assumptions more readily.
Optimisation: can sometimes be used to provide the optimum set of assumptions that maximises or minimises the results
Check: can be used as a check on the Monte Carlo simulation
Complexity: some problems are too complicated for analytical methods
Monte Simulation:
Complexity: problems that are too complicated for analytical methods can be solved using Monte carlo simulation
Proxy: monte carlo provides a range of results, which can be replaced by proxy models, which are expected to be faster
Fake: produces only pseudo-random output not truly random
Accuracy: less accurate than analytical models
Time: cannot be used for continuous time problems as the time step has to be discretised
How can the analytical methods supplement the Monte Carlo Simulations
Used as check on any simulation methods by providing an alternative method for calculating some value e.g the mean and median
Describe why a model that accurately predicts the mean claim amount, may not be the best
model for predicting the future claims experience of the insurance company
When the claims distribution has scattered data in the tails, a model which appears to accurately fit the mean may end up underestimating claims received in the tails of the
distribution.
This may be a particular problem for large claims because the impact of underestimating large claims may be much more significant than the benefits of accurately
modelling the average (or small) claims.
Thus, in this instance, a model that may be less accurate for the mean claim, but which gives more weight to the tails, may be preferable.
This would particularly be true if the purpose of
the modelling exercise is to set solvency reserves.
Outline a proxy model
developed to provide results with reasonable accuracy
subsitute for running the full model
used to replace the Monte Carlo simulation
providers faster but less accurate results
