Its application initially started in physics (sometimes known as the Monte Carlo Method). It is now being applied in engineering, life sciences, social sciences, and finance. See also Economic capital
So the valuation of an insurer involves a set of projections, looking at what is expected to happen, and thus coming up with the best estimate for assets and liabilities, and therefore for the company's level of solvency.
The projections in financial analysis usually use the most likely rate of claim, the most likely investment return, the most likely rate of inflation, and so on. The projections in engineering analysis usually use both the mostly likely rate and the most critical rate. The result provides a point estimate - the best single estimate of what the company's current solvency position is or multiple points of estimate - depends on the problem definition. Selection and identification of parameter values are frequently a challenge to less experienced analysts.
The downside of this approach is it does not fully cover the fact that there is a whole range of possible outcomes and some are more probable and some are less.
Based on a set of random outcomes, the experience of the policy/portfolio/company is projected, and the outcome is noted. Then this is done again with a new set of random variables. In fact, this process is repeated thousands of times.
At the end, a distribution of outcomes is available which shows not only what the most likely estimate, but what ranges are reasonable too.
This is useful when a policy or fund provides a guarantee, e.g. a minimum investment return of 5% per annum. A deterministic simulation, with varying scenarios for future investment return, does not provide a good way of estimating the cost of providing this guarantee. This is because it does not allow for the volatility of investment returns in each future time period or the chance that an extreme event in a particular time period leads to an investment return less than the guarantee. Stochastic modelling builds volatility and variability (randomness) into the simulation and therefore provides a better representation of real life from more angles.
For example, in application, applying the best estimate (defined as the mean) of investment returns to discount a set of cash flows will not necessarily give the same result as assessing the best estimate to the discounted cash flows.
A stochastic model would be able to assess this latter quantity with simulations.
This idea is seen again when one considers percentiles (see percentile). When assessing risks at specific percentiles, the factors that contribute to these levels are rarely at these percentiles themselves. Stochastic models can be simulated to assess the percentiles of the aggregated distributions.
Truncating and censoring of data can also be estimated using stochastic models. For instance, applying a non-proportional reinsurance layer to the best estimate losses will not necessarily give us the best estimate of the losses after the reinsurance layer. In a simulated stochastic model, the simulated losses can be made to "pass through" the layer and the resulting losses assessed appropriately.
The models and underlying parameters are chosen so that they fit historical economic data, and are expected to produce meaningful future projections.
Depending on the portfolios under investigation, a model can simulate all or some of the following factors stochastically:
Claims inflations can be applied, based on the inflation simulations that are consistent with the outputs of the asset model, as are dependencies between the losses of different portfolios.
The relative uniqueness of the policy portfolios written by a company in the general insurance sector means that claims models are typically tailor-made.
Estimating future claims liabilities might also involve estimating the uncertainty around the estimates of claim reserves.
See J Li's article "Comparison of Stochastic Reserving Models" (published in the Australian Actuarial Journal, volume 12 issue 4) for a recent article on this topic.