# Adaptive Multilevel Monte Carlo for Probabilities

@article{HajiAli2022AdaptiveMM, title={Adaptive Multilevel Monte Carlo for Probabilities}, author={Abdul-Lateef Haji-Ali and Jonathan D. Spence and Aretha L. Teckentrup}, journal={ArXiv}, year={2022}, volume={abs/2107.09148} }

. We consider the numerical approximation of P [ G ∈ Ω] where the d -dimensional 3 random variable G cannot be sampled directly, but there is a hierarchy of increasingly accurate 4 approximations { G ℓ } ℓ ∈ N which can be sampled. The cost of standard Monte Carlo estimation scales 5 poorly with accuracy in this setup since it compounds the approximation and sampling cost. A direct 6 application of Multilevel Monte Carlo improves this cost scaling slightly, but returns sub-optimal 7…

## 3 Citations

### Multilevel Monte Carlo combined with numerical smoothing for robust and efficient option pricing and density estimation

- Computer Science
- 2020

The employed numerical smoothing technique is applied to solve a broad class of problems, particularly for approximating distribution functions, ﬁnancial Greeks computation, and risk estimation and improves the complexity and robustness of the multilevel Monte Carlo method.

### Adaptive multilevel subset simulation with selective refinement

- Computer ScienceArXiv
- 2022

An adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems is proposed, using a posteriori error estimators combined with a selective mesh reﬁnement strategy to guarantee the critical subset property that may be violated when changing model resolution from one failure set to the next.

### Multilevel Path Branching for Digital Options

- Mathematics
- 2022

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…

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