Stochastic processes adapted by neural networks with application to climate, energy, and finance

Giebel, Stefan
Rainer, Martin
Local climate parameters may naturally effect the price of many commodities and their derivatives. Therefore we propose a joint framework for stochastic modeling of climate and commodity prices. In our setting, a stable Levy process is drift augmented to a generalized SDE. The related nonlinear function on the state space typically exhibits deterministic chaos. Additionally, a neural network adapts the parameters of the stable process such that the latter produces increasingly optimal differences between simulated output and observed data. Thus we propose a novel method of "intelligent'' calibration of the stochastic process, using learning neural networks in order to dynamically adapt the parameters of the stochastic model.


RMARS: Robustification of multivariate adaptive regression spline under polyhedral uncertainty
Ozmen, Ayse; Weber, Gerhard Wilhelm (Elsevier BV, 2014-03-15)
Since, with increased volatility and further uncertainties, financial crises translated a high "noise" within data from financial markets and economies into the related models, recent years' events in the financial world have led to radically untrustworthy representations of the future. Hence, robustification started to attract more attention in finance. The presence of noise and data uncertainty raises critical problems to be dealt with on the theoretical and computational side. For immunizing against para...
Analysis of volatility feedback and leverage effects on the ISE30 index using high frequency data
Inkaya, A.; Okur, Y. Yolcu (Elsevier BV, 2014-03-15)
In this study, we employ the techniques of Malliavin calculus to analyze the volatility feedback and leverage effects for a better understanding of financial market dynamics. We estimate both effects for a general semimartingale model applying Fourier analysis developed in Malliavin and Mancino (2002) [10]. We further investigate their joint behaviour using 5 min data of the ISE30 index. On the basis of these estimations, we look for the evidence that volatility feedback effect rate can be employed in the s...
On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift
Vardar Acar, Ceren; Szekely, Gabor J. (Elsevier BV, 2013-08-15)
Investors are naturally interested in the supremum and the infimum of stock prices, also in the maximum gain and the maximum loss over a time period. To shed light on these relatively complicated aspects of sample paths, we consider Brownian motion with and without drift. We provide explicit calculations of the correlation between the supremum and the infimum of Brownian motion with drift. We establish a number of results concerning the distributions of maximum gain and maximum loss. We present simulation s...
Scalar curvature and connected sums of self-dual 4-manifolds
Kalafat, Mustafa (European Mathematical Society Publishing House, 2011-01-01)
Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov-Lawson and Schoen-Yau in the self-dual category. The proof is based on twistor theory.
Nonlocal operators with local boundary conditions in higher dimensions
Aksoylu, Burak; Celiker, Fatih; Kilicer, Orsan (Springer Science and Business Media LLC, 2019-02-01)
We present novel nonlocal governing operators in 2D/3D for wave propagation and diffusion. The operators are inspired by peridynamics. They agree with the original peridynamics operator in the bulk of the domain and simultaneously enforce local boundary conditions (BC). The main ingredients are periodic, antiperiodic, and mixed extensions of separable kernel functions together with even and odd parts of bivariate functions on rectangular/box domains. The operators are bounded and self-adjoint. We present al...
Citation Formats
S. Giebel and M. Rainer, “Stochastic processes adapted by neural networks with application to climate, energy, and finance,” APPLIED MATHEMATICS AND COMPUTATION, pp. 1003–1007, 2011, Accessed: 00, 2020. [Online]. Available: