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  2. Monte Carlo methods in finance - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_methods_in_finance

    Essentially, the Monte Carlo method solves a problem by directly simulating the underlying (physical) process and then calculating the (average) result of the process. [ 1 ] This very general approach is valid in areas such as physics, chemistry, computer science etc. In finance, the Monte Carlo method is used to simulate the various sources of ...

  3. Metropolis–Hastings algorithm - Wikipedia

    en.wikipedia.org/wiki/Metropolis–Hastings...

    The Metropolis-Hastings algorithm sampling a normal one-dimensional posterior probability distribution. In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.

  4. Ensemble forecasting - Wikipedia

    en.wikipedia.org/wiki/Ensemble_forecasting

    Ensemble forecasting is a form of Monte Carlo analysis. The multiple simulations are conducted to account for the two usual sources of uncertainty in forecast models: (1) the errors introduced by the use of imperfect initial conditions, amplified by the chaotic nature of the evolution equations of the atmosphere, which is often referred to as ...

  5. Monte Carlo method - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_method

    Monte Carlo method: Pouring out a box of coins on a table, and then computing the ratio of coins that land heads versus tails is a Monte Carlo method of determining the behavior of repeated coin tosses, but it is not a simulation. Monte Carlo simulation: Drawing a large number of pseudo-random uniform variables from the interval [0,1] at one ...

  6. Multivariate statistics - Wikipedia

    en.wikipedia.org/wiki/Multivariate_statistics

    Multivariate statistics. Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis ...

  7. Kinetic Monte Carlo - Wikipedia

    en.wikipedia.org/wiki/Kinetic_Monte_Carlo

    Kinetic Monte Carlo. The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with known transition rates among states. These rates are inputs to the KMC algorithm; the method itself cannot predict them ...

  8. Monte Carlo methods for option pricing - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_methods_for...

    Contents. Monte Carlo methods for option pricing. In mathematical finance, a Monte Carlo option model uses Monte Carlo methods [ Notes 1 ] to calculate the value of an option with multiple sources of uncertainty or with complicated features. [ 1 ] The first application to option pricing was by Phelim Boyle in 1977 (for European options).

  9. Monte Carlo method in statistical mechanics - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_method_in...

    The general motivation to use the Monte Carlo method in statistical physics is to evaluate a multivariable integral. The typical problem begins with a system for which the Hamiltonian is known, it is at a given temperature and it follows the Boltzmann statistics. To obtain the mean value of some macroscopic variable, say A, the general approach ...

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