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pro vyhledávání: '"Giles, Michael B"'
Autor:
Giles, Michael B.
It is well known that the Euler-Maruyama discretisation of an autonomous SDE using a uniform timestep $h$ has a strong convergence error which is $O(h^{1/2})$ when the drift and diffusion are both globally Lipschitz. This note proves that the same is
Externí odkaz:
http://arxiv.org/abs/2411.15930
The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying valuation adjustm
Externí odkaz:
http://arxiv.org/abs/2301.05886
Autor:
Giles, Michael B
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower decay in the v
Externí odkaz:
http://arxiv.org/abs/2301.02882
We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underly
Externí odkaz:
http://arxiv.org/abs/2209.03017
Autor:
Croci, Matteo, Giles, Michael B.
Publikováno v:
IMA Journal of Numerical Analysis, April 2022
Motivated by the advent of machine learning, the last few years have seen the return of hardware-supported low-precision computing. Computations with fewer digits are faster and more memory and energy efficient, but can be extremely susceptible to ro
Externí odkaz:
http://arxiv.org/abs/2010.16225
Publikováno v:
Journal of Computational Finance, 26:1 (2022)
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenar
Externí odkaz:
http://arxiv.org/abs/1912.05484
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). In particular, most of the numerical approximation schemes studied in the scientific literature suffer
Externí odkaz:
http://arxiv.org/abs/1911.03188
Publikováno v:
SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 3, 1236-1259, 2020
We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under uncertainty. EVSI is defined as a nested expectation in which an outer
Externí odkaz:
http://arxiv.org/abs/1909.00549
We study the approximation of expectations $\operatorname{E}(f(X))$ for solutions $X$ of stochastic differential equations and functionals $f$ on the path space by means of Monte Carlo algorithms that only use random bits instead of random numbers. W
Externí odkaz:
http://arxiv.org/abs/1902.09984
We study the approximation of expectations $\E(f(X))$ for solutions $X$ of SDEs and functionals $f \colon C([0,1],\R^r) \to \R$ by means of restricted Monte Carlo algorithms that may only use random bits instead of random numbers. We consider the wor
Externí odkaz:
http://arxiv.org/abs/1808.10623