Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Smoothing with Hierarchical Adaptive Sparse Grids and
  Quasi-Monte Carlo Methods for Efficient Option Pricing   When approximating the expectation of a functional of a stochastic process,
the efficiency and performance of deterministic quadrature methods, such as
sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may critically
depend on the regularity of the integrand. To overcome this issue and reveal
the available regularity, we consider cases in which analytic smoothing cannot
be performed, and introduce a novel numerical smoothing approach by combining a
root finding algorithm with one-dimensional integration with respect to a
single well-selected variable. We prove that under appropriate conditions, the
resulting function of the remaining variables is a highly smooth function,
potentially affording the improved efficiency of adaptive sparse grid
quadrature (ASGQ) and QMC methods, particularly when combined with hierarchical
transformations (i.e., Brownian bridge and Richardson extrapolation on the weak
error). This approach facilitates the effective treatment of high
dimensionality. Our study is motivated by option pricing problems, and our
focus is on dynamics where the discretization of the asset price is necessary.
Based on our analysis and numerical experiments, we show the advantages of
combining numerical smoothing with the ASGQ and QMC methods over ASGQ and QMC
methods without smoothing and the Monte Carlo approach.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc