A numerical method simulating a large number of random scenarios to estimate the distribution of a quantity when analytical calculation is impossible.
Monte Carlo simulation is a numerical method that estimates the distribution of an uncertain quantity by generating a very large number of random scenarios and observing the spread of the results obtained. When the complexity of a problem precludes an exact analytical calculation, for example because multiple sources of uncertainty interact non-linearly, one simulates thousands or millions of draws, each representing a possible future, and then derives indicators such as the mean, the quantiles or measures of extreme risk. This approach has become a central tool of modern actuarial science and risk management, at the heart of internal solvency models, catastrophe models and the computation of measures such as value at risk. Its power lies in its flexibility, since almost any probabilistic problem can be tackled by simulation. Its fundamental limit is summed up by the adage that a result is worth only as much as its assumptions, the quality of the distributions and dependencies fed in entirely determining the reliability of the outputs. In cyber, where these assumptions, and notably the dependence structures, are poorly known, simulation produces results to be handled with particular caution.
To estimate the capital needed to cover a portfolio, an insurer simulates a million possible years, each with its losses drawn at random according to the chosen laws, then reads from the resulting distribution the loss that only the worst years exceed.
Monte-Carlo, simulation de Monte-Carlo, Monte Carlo simulation, méthode de Monte-Carlo