Principles of actuarial modelling Flashcards
14 Key Steps in a modelling process
Advantages of models
(SPE ISC3)
Models allow us to investigate the future behavior of a process in compressed time
Models allow us to study the stochastic nature of the results e.g using Monte Carlo simulation
Models allow us to consider scenarios that would not be feasible in practice e.g because of cost or other business considerations
Models allow control over experimental conditions so that we can reduce the variance of the results output without affecting the mean values
SPE
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
Different future policies or possible actions can be compared to see which best suits the requirements or constraints of the user
we can get control over the experimental conditions by reducing the variance without upsetting their mean values
Disadvantages
Models can be time-consuming and expensive to set up
Stochastic models require a large number of simulations to be carried out to get accurate results
In general, models are more useful for comparing the results of input variations than optimising outputs
Models can give an impression of greater accuracy and reliability than they actually have and so may create a sense of false security
The results from models are dependent on the data used which may be inaccurate and unreliable
Users of the model may not understand fully how it works and its limitations
Models may not capture sufficiently accurately the real world situation
Models require simplifying assumptions that might turn out wrong e,g may ignore certain features or certain types of events that could occur
Some models may be difficult to explain to clients
Suitability of a model
OV3 PC2R C2RAE
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
Deterministic vs Stochastic
A stochastic model is one the recognises the random nature of the variable. A deterministic does not contain any random component.
With a deterministic model, the output is determined once the set of fixed input and the relationship between them have been defined. However with a stochastic model, output is random in nature, like the input. The output is only an estimate of the characteristics of the model for a given set of inputs.
So several independent runs are required for each set of inputs.
A deterministic model is simplified case of a stochastic model
Issues/parameters to consider when modelling a life office
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 analysis 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)
