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On optimal thresholds for pairs trading in a one-dimensional diffusion model
No full textWe study the static maximization of long-term averaged profit, when optimal preset thresholds are determined to describe a pairs trading strategy in a general one-dimensional ergodic diffusion model of a stochastic spread process. An explicit formula for the expected value of a certain first passage time is given, which is used to derive a simple equation for determining the optimal thresholds. Asymptotic arbitrage in the long run of the threshold strategy is observed.
doi:10.1017/S144618112100029
Uncertainty quantification for the Hokkaido Nansei-Oki tsunami using B-splines on adaptive sparse grids
Get PDFModeling uncertainties in the input parameters of computer simulations is an established way to account for inevitably limited knowledge. To overcome long run-times and high demand for computational resources, a surrogate model can replace the original simulation. We use spatially adaptive sparse grids for the creation of this surrogate model. Sparse grids are a discretization scheme designed to mitigate the curse of dimensionality, and spatial adaptivity further decreases the necessary number of expensive simulations. We combine this with B-spline basis functions which provide gradients and are exactly integrable. We demonstrate the capability of this uncertainty quantification approach for a simulation of the Hokkaido Nansei–Oki Tsunami with anuga. We develop a better understanding of the tsunami behavior by calculating key quantities such as mean, percentiles and maximum run-up. We compare our approach to the popular Dakota toolbox and reach slightly better results for all quantities of interest.
References
B. M. Adams, M. S. Ebeida, et al. Dakota. Sandia Technical Report, SAND2014-4633, Version 6.11 User’s Manual, July 2014. 2019. https://dakota.sandia.gov/content/manuals.
J. H. S. de Baar and S. G. Roberts. Multifidelity sparse-grid-based uncertainty quantification for the Hokkaido Nansei–Oki tsunami. Pure Appl. Geophys. 174 (2017), pp. 3107–3121. doi: 10.1007/s00024-017-1606-y.
H.-J. Bungartz and M. Griebel. Sparse grids. Acta Numer. 13 (2004), pp. 147–269. doi: 10.1017/S0962492904000182.
M. Eldred and J. Burkardt. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA. 2009. doi: 10.2514/6.2009-976.
K. Höllig and J. Hörner. Approximation and modeling with B-splines. Philadelphia: SIAM, 2013. doi: 10.1137/1.9781611972955.
M. Matsuyama and H. Tanaka. An experimental study of the highest run-up height in the 1993 Hokkaido Nansei–Oki earthquake tsunami. National Tsunami Hazard Mitigation Program Review and International Tsunami Symposium (ITS). 2001.
O. Nielsen, S. Roberts, D. Gray, A. McPherson, and A. Hitchman. Hydrodymamic modelling of coastal inundation. MODSIM 2005. 2005, pp. 518–523. https://www.mssanz.org.au/modsim05/papers/nielsen.pdf.
J. Nocedal and S. J. Wright. Numerical optimization. Springer, 2006. doi: 10.1007/978-0-387-40065-5.
D. Pflüger. Spatially Adaptive Sparse Grids for High-Dimensional Problems. Dr. rer. nat., Technische Universität München, Aug. 2010. https://www5.in.tum.de/pub/pflueger10spatially.pdf.
M. F. Rehme, F. Franzelin, and D. Pflüger. B-splines on sparse grids for surrogates in uncertainty quantification. Reliab. Eng. Sys. Saf. 209 (2021), p. 107430. doi: 10.1016/j.ress.2021.107430.
M. F. Rehme and D. Pflüger. Stochastic collocation with hierarchical extended B-splines on Sparse Grids. Approximation Theory XVI, AT 2019. Springer Proc. Math. Stats. Vol. 336. Springer, 2020. doi: 10.1007/978-3-030-57464-2_12.
S Roberts, O. Nielsen, D. Gray, J. Sexton, and G. Davies. ANUGA. Geoscience Australia. 2015. doi: 10.13140/RG.2.2.12401.99686.
I. J. Schoenberg and A. Whitney. On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves. Trans. Am. Math. Soc. 74.2 (1953), pp. 246–259. doi: 10.2307/1990881.
W. Sickel and T. Ullrich. Spline interpolation on sparse grids. Appl. Anal. 90.3–4 (2011), pp. 337–383. doi: 10.1080/00036811.2010.495336.
C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kânoğlu, and F. I. González. Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models. NOAA/Pacific Marine Environmental Laboratory. 2007. https://nctr.pmel.noaa.gov/benchmark/.
J. Valentin and D. Pflüger. Hierarchical gradient-based optimization with B-splines on sparse grids. Sparse Grids and Applications—Stuttgart 2014. Lecture Notes in Computational Science and Engineering. Vol. 109. Springer, 2016, pp. 315–336. doi: 10.1007/978-3-319-28262-6_13.
D. Xiu and G. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24.2 (2002), pp. 619–644. doi: 10.1137/S1064827501387826
Finite -groups and coclass theory
No full textThis article is the abstract for the Ph.D. thesis of Subhrajyoti Saha. Doctor of Philosophy was awarded to Subhrajyoti Saha on the basis of this thesis by Monash University. In this article, we present the abstract for the thesis along with the necessary references
Efficient polynomial chaos approximations: Active, local and basis-adapted
Get PDFMetamodels provide an efficient means for the approximation of response surfaces of systems, particularly for resource-intensive experiment designs. It is oftentimes the case that interest is focused on a specific region of the parameter space. We propose an efficient recipe for the local approximation of response surfaces using Polynomial Chaos techniques. For systems embedded in high-dimensional settings, a basis-adapted spectral representation is exploited locally for dimension reduction. The proposed approach comprises an initial heuristic global solution for parameter space exploration using an approximate global Polynomial Chaos metamodel, followed by a local design being refined through an active learning scheme. The problem of turbulent flow around a symmetric airfoil is considered. Statistical estimators based on the local, active, basis-adapted approach show less bias and faster convergence as compared to the estimators from a global solution.
References
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Z. G. Ghauch. Leveraging adapted polynomial chaos metamodels for real-time Bayesian updating. J. Verif. Valid. Uncert. 4(4):041003, 2020. doi: 10.1115/1.4045693.
Z. G. Ghauch, V. Aitharaju, W. R. Rodgers, P. Pasupuleti, A. Dereims, and R. G. Ghanem. Integrated stochastic analysis of fiber composites manufacturing using adapted polynomial chaos expansions. Compos. Part A: Appl. Sci. 118:179–193, 2019. doi: 10.1016/j.compositesa.2018.12.029.
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C. Thimmisetty, P. Tsilifis, and R. Ghanem. Homogeneous chaos basis adaptation for design optimization under uncertainty: Application to the oil well placement problem. AI EDAM 31(3):265–276, 2017. doi: 10.1017/S0890060417000166.
R. Tipireddy and R. Ghanem. Basis adaptation in homogeneous chaos spaces. J. Comput. Phys. 259:304–317, 2014. doi: 10.1016/j.jcp.2013.12.009.
P. Tsilifis and R. G. Ghanem. Reduced Wiener chaos representation of random fields via basis adaptation and projection. J. Comput. Phys. 341:102–120, 2017. doi: 10.1016/j.jcp.2017.04.009.
Turbulence Modeling Resource. NASA Langley Research Center. Washington, DC, 2018. http://turbmodels.larc.nasa.gov/
On Graev's theorem for free products of Hausdorff topological groups
No full texthttp://dx.doi.org/10.1017/S000497271200033
Arithmetic properties of -regular partitions in -colours
No full texthttp://dx.doi.org/10.1017/S000497271200033
Pointwise residual method for solving primal and dual ill-posed linear programming problems with approximate data
No full textWe propose a variation of the pointwise residual method for solving primal and dual ill-posed linear programming with approximate data, sensitive to small perturbations. The method leads to an auxiliary problem, which is also a linear programming problem. Theorems of existence and convergence of approximate solutions are established and optimal estimates of approximation of initial problem solutions are achieved.
doi:10.1017/S144618112000024
Modelling human carrying capacity as a function of food availability
No full textWe assume that human carrying capacity is determined by food availability. We propose three classes of human population dynamical models of logistic type, where the carrying capacity is a function of the food production index. We also employ an integration-based parameter estimation technique to derive explicit formulas for the model parameters. Using actual population and food production index data, numerical simulations of our models suggest that an increase in food availability implies an increase in carrying capacity, but the carrying capacity is “self-limiting” and does not increase indefinitely.
doi:10.1017/S144618112000020
Multinomial Vandermonde convolution via permanent
No full textA generalized Laplace expansion for the permanent function is provided. As a consequence, a multinomial Vandermonde convolution is reproved. Some combinatorial identities are derived by applying some special matrices to the expansion.
http://dx.doi.org/10.1017/S000497271200033
