The Monte Carlo Simulation
The behavior of stochastic processes is studied by applying the Monte Carlo Simulation method. All inputs are stochastic in solving these type of problems. The MCS is particularly useful if the processes are nonlinear or may involve innumerable uncertain inputs, that are distributed differently from each other (Hartford and Baecher 2004). The MCS generates a number of sets of randomly generated values for the uncertain parameters and quantifies the performance function of each applicable set. A CDF (Cumulative Distributive Function) can be plotted from these random samples and values for the variance and higher moments can be estimated. irrespective of the number of inputs, each run will give us a single observation of the process. hence, just increasing the number of stochastic inputs will not increase the number of funds for a given accuracy that can be inferred by using statistical methods.
The size and complexity of a model dictates the number of iterations needed in a given simulation. By keeping track of the stability of the output distributions being generated, it is possible to determine the adequate number of iterations required. Typically, output distributions become more stable as the number of iterations per simulation is increased. This is because as the sample size increases and the distribution change less. The simulation process may be stopped when the statistics change less than a percentage of the convergence (e.g. 15). The parameters considered for this test are the standard deviation, the mean and the percentiles ( 5% to 95% in 5% increments) of each output.
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