29,401 research outputs found
Importance sampling for option pricing with feedforward neural networks
We study the problem of reducing the variance of Monte Carlo estimators
through performing suitable changes of the sampling measure which are induced
by feedforward neural networks. To this end, building on the concept of vector
stochastic integration, we characterize the Cameron-Martin spaces of a large
class of Gaussian measures which are induced by vector-valued continuous local
martingales with deterministic covariation. We prove that feedforward neural
networks enjoy, up to an isometry, the universal approximation property in
these topological spaces. We then prove that sampling measures which are
generated by feedforward neural networks can approximate the optimal sampling
measure arbitrarily well. We conclude with a comprehensive numerical study
pricing path-dependent European options for asset price models that incorporate
factors such as changing business activity, knock-out barriers, dynamic
correlations, and high-dimensional baskets
Learning feedforward controller for a mobile robot vehicle
This paper describes the design and realisation of an on-line learning posetracking controller for a three-wheeled mobile robot vehicle. The controller consists of two components. The first is a constant-gain feedback component, designed on the basis of a second-order model. The second is a learning feedforward component, containing a single-layer neural network, that generates a control contribution on the basis of the desired trajectory of the vehicle. The neural network uses B-spline basis functions, enabling a computationally fast implementation and fast learning. The resulting control system is able to correct for errors due to parameter mismatches and classes of structural errors in the model used for the controller design. After sufficient learning, an existing static gain controller designed on the basis of an extensive model has been outperformed in terms of tracking accuracy
Brain rhythms of pain
Pain is an integrative phenomenon that results from dynamic interactions between sensory and contextual (i.e., cognitive, emotional, and motivational) processes. In the brain the experience of pain is associated with neuronal oscillations and synchrony at different frequencies. However, an overarching framework for the significance of oscillations for pain remains lacking. Recent concepts relate oscillations at different frequencies to the routing of information flow in the brain and the signaling of predictions and prediction errors. The application of these concepts to pain promises insights into how flexible routing of information flow coordinates diverse processes that merge into the experience of pain. Such insights might have implications for the understanding and treatment of chronic pain
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