78,048 research outputs found
Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis
We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis
(GSA) techniques to pricing and risk management (greeks) of representative
financial instruments of increasing complexity. We compare QMC vs standard
Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low
discrepancy sequences, different discretization methods, and specific analyses
of convergence, performance, speed up, stability, and error optimization for
finite differences greeks. We find that our QMC outperforms MC in most cases,
including the highest-dimensional simulations and greeks calculations, showing
faster and more stable convergence to exact or almost exact results. Using GSA,
we are able to fully explain our findings in terms of reduced effective
dimension of our QMC simulation, allowed in most cases, but not always, by
Brownian bridge discretization. We conclude that, beyond pricing, QMC is a very
promising technique also for computing risk figures, greeks in particular, as
it allows to reduce the computational effort of high-dimensional Monte Carlo
simulations typical of modern risk management.Comment: 43 pages, 21 figures, 6 table
Model fusion using fuzzy aggregation: Special applications to metal properties
To improve the modelling performance, one should either propose a new modelling methodology or make the best of existing models. In this paper, the study is concentrated on the latter solution, where a structure-free modelling paradigm is proposed. It does not rely on a fixed structure and can combine various modelling techniques in âsymbiosisâ using a âmaster fuzzy systemâ. This approach is shown to be able to include the advantages of different modelling techniques altogether by requiring less training and by minimising the efforts relating optimisation of the final structure. The proposed approach is then successfully applied to the industrial problems of predicting machining induced residual stresses for aerospace alloy components as well as modelling the mechanical properties of heat-treated alloy steels, both representing complex, non-linear and multi-dimensional environments
Forward-Mode Automatic Differentiation in Julia
We present ForwardDiff, a Julia package for forward-mode automatic
differentiation (AD) featuring performance competitive with low-level languages
like C++. Unlike recently developed AD tools in other popular high-level
languages such as Python and MATLAB, ForwardDiff takes advantage of
just-in-time (JIT) compilation to transparently recompile AD-unaware user code,
enabling efficient support for higher-order differentiation and differentiation
using custom number types (including complex numbers). For gradient and
Jacobian calculations, ForwardDiff provides a variant of vector-forward mode
that avoids expensive heap allocation and makes better use of memory bandwidth
than traditional vector mode. In our numerical experiments, we demonstrate that
for nontrivially large dimensions, ForwardDiff's gradient computations can be
faster than a reverse-mode implementation from the Python-based autograd
package. We also illustrate how ForwardDiff is used effectively within JuMP, a
modeling language for optimization. According to our usage statistics, 41
unique repositories on GitHub depend on ForwardDiff, with users from diverse
fields such as astronomy, optimization, finite element analysis, and
statistics.
This document is an extended abstract that has been accepted for presentation
at the AD2016 7th International Conference on Algorithmic Differentiation.Comment: 4 page
Open-ended evolution to discover analogue circuits for beyond conventional applications
This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s10710-012-9163-8. Copyright @ Springer 2012.Analogue circuits synthesised by means of open-ended evolutionary algorithms often have unconventional designs. However, these circuits are typically highly compact, and the general nature of the evolutionary search methodology allows such designs to be used in many applications. Previous work on the evolutionary design of analogue circuits has focused on circuits that lie well within analogue application domain. In contrast, our paper considers the evolution of analogue circuits that are usually synthesised in digital logic. We have developed four computational circuits, two voltage distributor circuits and a time interval metre circuit. The approach, despite its simplicity, succeeds over the design tasks owing to the employment of substructure reuse and incremental evolution. Our findings expand the range of applications that are considered suitable for evolutionary electronics
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