A review of efficient Multilevel Monte Carlo algorithms for derivative pricing and risk management [PDF]
MethodsX, 2023 In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithms, in the paradigm of applications in financial engineering.
Devang Sinha, Siddhartha P. Chakrabarty
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Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems. [PDF]
J Sci Comput, 2023 We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection–diffusion operator with random coefficients.
Cui T +4 more
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Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media [PDF]
Royal Society Open Science, 2017 In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during ...
D. Crevillén-García, H. Power
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Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance [PDF]
Quantum, 2021 Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs).
Dong An +5 more
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A multilevel Monte Carlo finite element method for the stochastic Cahn-Hilliard-Cook equation. [PDF]
Comput Mech, 2019 In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn–Hilliard–Cook equation. The Ciarlet–Raviart mixed finite element method is applied to solve the fourth-order equation.
Khodadadian A +5 more
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A Multilevel Monte Carlo Method for Performing Time-Variant Reliability Analysis
IEEE Access, 2021 Even though a great number of methods have been developed for time-variant reliability analysis (TRA), crude Monte Carlo simulation (MCS) is still widely used alone or combined with other methods to enhance the efficiency and accuracy of TRA.
Jian Wang +3 more
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An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson system [PDF]
Computer Methods in Applied Mechanics and Engineering, 2020 We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift-diffusion-Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial ...
Heitzinger, Clemens +2 more
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Multilevel Monte Carlo FEM for elliptic PDEs with Besov random tree priors [PDF]
Stochastics and Partial Differential Equations: Analysis and Computations, 2023 We develop a multilevel Monte Carlo (MLMC)-FEM algorithm for linear, elliptic diffusion problems in polytopal domain D⊂Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}
C. Schwab, A. Stein
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Unbiased Multilevel Monte Carlo methods for intractable distributions: MLMC meets MCMC [PDF]
Journal of machine learning research, 2022 Constructing unbiased estimators from Markov chain Monte Carlo (MCMC) outputs is a difficult problem that has recently received a lot of attention in the statistics and machine learning communities. However, the current unbiased MCMC framework only works
Guanyang Wang, T. Wang
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Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem [PDF]
Computer Physics Communications, 2023 The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad--Shafranov equation.
H. Elman +2 more
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