Improved Multilevel Monte Carlo Convergence using the Milstein Scheme

By M. Giles. 2008

257 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics, Finance

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “Heinrich, 2001; Giles, 2008), and (viii) a plethora of sophisticated Markov chain Monte Carlo sampling schemes. Reviews of many of the above techniques can be found in Glasserman (2004) as well as Rubinstein and Kroese (2011).”
Characterization of bistability for stochastic multistep methods (2010, unknown): “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.”
Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011, methodology): “This family of methods was introduced, to the authors’ knowledge, by Giles [17,18] for Itô stochastic ordinary differential equations after earlier work by Heinrich on numerical quadrature (see [21]).”
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011, methodology): “Our approach is based on the multilevel Monte Carlo method (MLMC) for infinitedimensional integration introduced by Giles in connection with stochastic differential equations arising in mathematical finance [13, 12].”
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 Multidimensional SDEs (2013, methodology): “A better treatment, which is the one used in [3], is to use the conditional Monte Carlo approach to further smooth the payoff.”
An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process (2012, methodology): “Here, the knowledge of the global strong convergence rate of the approximation is important, in particular, if the efficient multi-level Monte Carlo method (Giles 2007, 2008) is to be used.”