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Multilevel Monte Carlo Methods for Simulated Maximum Likelihood Inference in Multivariate Diffusions

Lindström, Erik LU orcid and Åkerlindh, Carl LU (2016) WORLD CONGRESS OF THE BACHELIER FINANCE SOCIETY
Abstract
Multilevel Monte Carlo is a novel method for reducing the computational cost when computing conditional expectations of stochastic processes. This paper considers the transition density for diffusion processes. It is known that the transition density can be written as an expectation by utilizing the law of total probability combined with the Markov property. This idea is combined with the multilevel Monte Carlo framework to derive a new estimator. Both the theoretical derivation and the simulations show that the proposed method is able to reduce the variance of the estimates substantially, when keeping the bias and computational cost fixed, relative to the standard approximations.









Abstract (Swedish)
Multilevel Monte Carlo is a novel method for reducing the computational cost
when computing conditional expectations of stochastic processes. This paper considers
the transition density for diffusion processes. It is known that the transition
density can be written as an expectation by utilizing the law of total probability
combined with the Markov property. This idea is combined with the multilevel
Monte Carlo framework to derive a new estimator.
Both the theoretical derivation and the simulations show that the proposed
method is able to reduce the variance of the estimates substantially, when keeping
the bias and computational cost fixed, relative to the standard approximations.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to conference
publication status
published
subject
conference name
WORLD CONGRESS OF THE BACHELIER FINANCE SOCIETY
conference location
New York, United States
conference dates
2016-07-15 - 2016-07-19
language
English
LU publication?
yes
id
e0ebfbe0-b6b3-4b74-9e19-169448425e9b
date added to LUP
2017-10-26 16:38:03
date last changed
2019-03-08 03:24:08
@misc{e0ebfbe0-b6b3-4b74-9e19-169448425e9b,
  abstract     = {{Multilevel Monte Carlo is a novel method for reducing the computational cost when computing conditional expectations of stochastic processes. This paper considers the transition density for diffusion processes. It is known that the transition density can be written as an expectation by utilizing the law of total probability combined with the Markov property. This idea is combined with the multilevel Monte Carlo framework to derive a new estimator. Both the theoretical derivation and the simulations show that the proposed method is able to reduce the variance of the estimates substantially, when keeping the bias and computational cost fixed, relative to the standard approximations.<br/><br/><br/><br/><br/><br/><br/><br/><br/><br/>}},
  author       = {{Lindström, Erik and Åkerlindh, Carl}},
  language     = {{eng}},
  title        = {{Multilevel Monte Carlo Methods for Simulated Maximum Likelihood Inference in Multivariate Diffusions}},
  year         = {{2016}},
}