Generalization of a theorem of Gonchar

Let $X, Y$ be two complex manifolds, let $D\subset X,$ $G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Under a geometric condition on the boundary sets $A$ and $B,$ we show that every function locally bounded, separately continuous on $W,$ continuous on $A\times B,$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a function continuous on a "domain of holomorphy" $\hat{W}$ and holomorphic on the interior of $\hat{W}.$Comment: 14 pages, to appear in Arkiv for Matemati

Derivatives of Markov kernels and their Jordan decomposition

We study a particular class of transition kernels that stems from differentiating Markov kernels in the weak sense. Sufficient conditions are established for this type of kernels to admit a Jordan-type decomposition. The decomposition is explicitly constructed. © Heldermann Verlag

Portfolio Optimization Using SPEA2 with Resampling

Proceeding of: Intelligent Data Engineering and Automated Learning – IDEAL 2011: 12th International Conference, Norwich, UK, September 7-9, 2011The subject of financial portfolio optimization under real-world constraints is a difficult problem that can be tackled using multiobjective evolutionary algorithms. One of the most problematic issues is the dependence of the results on the estimates for a set of parameters, that is, the robustness of solutions. These estimates are often inaccurate and this may result on solutions that, in theory, offered an appropriate risk/return balance and, in practice, resulted being very poor. In this paper we suggest that using a resampling mechanism may filter out the most unstable. We test this idea on real data using SPEA2 as optimization algorithm and the results show that the use of resampling increases significantly the reliability of the resulting portfolios.The authors acknowledge financial support granted by the Spanish Ministry of Science under contract TIN2008-06491-C04-03 (MSTAR) and Comunidad de Madrid (CCG10- UC3M/TIC-5029).Publicad

Evolutionary multi-stage financial scenario tree generation

Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations (represented as scenario trees) have been suggested in the literature. In this paper, a new evolutionary algorithm to create scenario trees for multi-stage financial optimization models will be presented. Numerical results and implementation details conclude the paper

Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

Mean-risk models using two risk measures: A multi-objective approach

This paper proposes a model for portfolio optimisation, in which distributions are characterised and compared on the basis of three statistics: the expected value, the variance and the CVaR at a specified confidence level. The problem is multi-objective and transformed into a single objective problem in which variance is minimised while constraints are imposed on the expected value and CVaR. In the case of discrete random variables, the problem is a quadratic program. The mean-variance (mean-CVaR) efficient solutions that are not dominated with respect to CVaR (variance) are particular efficient solutions of the proposed model. In addition, the model has efficient solutions that are discarded by both mean-variance and mean-CVaR models, although they may improve the return distribution. The model is tested on real data drawn from the FTSE 100 index. An analysis of the return distribution of the chosen portfolios is presented

Technical note: Introduction of a superconducting gravimeter as novel hydrological sensor for the Alpine research catchment Zugspitze

GFZ (German Research Centre for Geosciences) set up the Zugspitze Geodynamic Observatory Germany with a worldwide unique installation of a superconducting gravimeter at the summit of Mount Zugspitze on top of the Partnach spring catchment. This high alpine catchment is well instrumented, acts as natural lysimeter and has significant importance for water supply to its forelands, with a large mean annual precipitation of 2080ĝ€¯mm and a long seasonal snow cover period of 9 months, while showing a high sensitivity to climate change. However, regarding the majority of alpine regions worldwide, there is only limited knowledge on temporal water storage variations due to sparsely distributed hydrological and meteorological sensors and the large variability and complexity of signals in alpine terrain. This underlines the importance of well-equipped areas such as Mount Zugspitze serving as natural test laboratories for improved monitoring, understanding and prediction of alpine hydrological processes. The observatory superconducting gravimeter, OSG 052, supplements the existing sensor network as a novel hydrological sensor system for the direct observation of the integral gravity effect of total water storage variations in the alpine research catchment at Zugspitze. Besides the experimental set-up and the available data sets, the gravimetric methods and gravity residuals are presented based on the first 27 months of observations from 29 December 2018 to 31 March 2021. The snowpack is identified as being a primary contributor to seasonal water storage variations and, thus, to the gravity residuals with a signal range of up to 750ĝ€¯nms-2 corresponding to 1957ĝ€¯mm snow water equivalent measured with a snow scale at an altitude of 2420ĝ€¯m at the end of May 2019. Hydro-gravimetric sensitivity analysis reveal a snow-gravimetric footprint of up to 4ĝ€¯km distance around the gravimeter, with a dominant gravity contribution from the snowpack in the Partnach spring catchment. This shows that the hydro-gravimetric approach delivers representative integral insights into the water balance of this high alpine site. © Copyright

HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems

A remark on the dimension of the Bergman space of some Hartogs domains

Let D be a Hartogs domain of the form D={(z,w) \in CxC^N : |w| < e^{-u(z)}} where u is a subharmonic function on C. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite dimensional.Comment: 12 page