Nesting Monte Carlo for high-dimensional non-linear PDEs
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Xavier Warin
Abstract
A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Depending on the type of non-linearity, different schemes are proposed and theoretically studied: variance error are given and it is shown that the bias of the schemes can be controlled. The limitation of the method is that the maturity or the Lipschitz constants of the non-linearity should not be too high in order to avoid an explosion of the computational time. Many numerical results are given in high dimension for cases where analytical solutions are available or where some solutions can be computed by deep-learning methods.
Funding statement: This work has benefited from the financial support of the ANR Caesars and ANR program “Investissement d’avenir”.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Nesting Monte Carlo for high-dimensional non-linear PDEs
- Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero
- Global sensitivity analysis for a stochastic flow problem
- Sampling from the 𝒢I0 distribution
- A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation
- On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters
- Random walk algorithms for elliptic equations and boundary singularities
Articles in the same Issue
- Frontmatter
- Nesting Monte Carlo for high-dimensional non-linear PDEs
- Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero
- Global sensitivity analysis for a stochastic flow problem
- Sampling from the 𝒢I0 distribution
- A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation
- On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters
- Random walk algorithms for elliptic equations and boundary singularities
