Multilevel Monte Carlo Path Simulation

By M. Giles. Operational Research, 2008

1,613 citations recorded by the source corpus.

Subfields: Finance, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9011df67b7e93b0727162b0778517e068cfbf902

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Citations in the corpus

Characterization of bistability for stochastic multistep methods (2010, positive): “Moreover, Giles [10, 11] showed that the strong convergence is also essential for developing efficient multilevel Monte Carlo methods, which are applied to problems where the weak error is considered.”
Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients (2013, background): “It is fruitful to consider the strong convergence because: pathwise convergence, relevant for assets models in mathematical finance, follows automatically [20]; efficient Monte Carlo simulations relay on both weak and strong convergence, for example, multilevel Monte Carlo methods [11,19].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “A multifidelity method that combines outputs from computationally cheap low-fidelity models with outputs from the high-fidelity model can lead to significant reductions in runtime and provide unbiased estimators of the statistics of the high-fidelity model outputs [76, 150, 148, 198, 160].”
A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations (2011, methodology): “When γ = 1/2 in (ii), the asymptotics are the same as in the classical diffusion setting analyzed in [Gil08b].”
A note on tamed Euler approximations (2013, background): “Submitted to ECP on May 21, 2013, final version accepted on May 31, 2013.”
Multifidelity importance sampling (2016, methodology): “One approach based on the control variate method is the multi-level Monte Carlo method [15, 16], which combines the outputs of a hierarchy of coarse grid solutions using control variates.”
Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model (2011, background): “– weak convergence [17] and pathwise convergence [16] follow automatically, and – efficient multi-level Monte Carlo simulations rely on both weak and strong convergence properties [ 11 , 12].”
Multilevel Richardson-Romberg Extrapolation (2014, methodology): “These assumptions are the basement of multilevel simulation methods (see [Gil08, Hei01]): Bias error expansion (weak error rate): where c k , k = 1 , . . . , ¯ R are real coeﬃcients and η ¯ R is a real valued function deﬁned on H .”
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011, background): “Let us recall the main ideas and the main theorem from [Giles, 2008].”
On Nesting Monte Carlo Estimators (2017, methodology): “Also related is the study of techniques for variance reduction, such as multilevel MC (Heinrich, 2001; Giles, 2008), and bias reduction, such as the multi-step Richardson-Romberg method (Pages, 2007; Lemaire et al., 2017) and Russian roulette sampling (Lyne et al., 2015), many of which are…”
Multi-Level {M}onte {C}arlo Algorithms for Infinite-Dimensional Integration on $\mathbb{R}^\mathbb{N}$ (2010, methodology): “Recently, multi-level algorithms have been employed for finite- as well as for infinitedimensional integration, starting with Heinrich (1998, 2001) and Giles (2008a, 2008b).”
Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation (2012, methodology): “Here we recall the theorem from [8] (which is a slight generalisation of the original theorem in [6]) which gives the complexity of MLMC estimation.”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “Recent applications with American options can be found in [34, 101], and novel approaches for option pricing that allow one to use control variates for which the expectation is not known are studied in [139, 426].”