Optimal XL-insurance under Wasserstein-type ambiguity

We study the problem of optimal insurance contract design for risk management under a budget constraint. The contract holder takes into consideration that the loss distribution is not entirely known and therefore faces an ambiguity problem. For a given set of models, we formulate a minimax optimization problem of finding an optimal insurance contract that minimizes the distortion risk functional of the retained loss with premium limitation. We demonstrate that under the average value-at-risk measure, the entrance-excess of loss contracts are optimal under ambiguity, and we solve the distributionally robust optimal contract-design problem. It is assumed that the insurance premium is calculated according to a given baseline loss distribution and that the ambiguity set of possible distributions forms a neighborhood of the baseline distribution. To this end, we introduce a contorted Wasserstein distance. This distance is finer in the tails of the distributions compared to the usual Wasserstein distance

Comfort-oriented control strategies for decentralized ventilation using co-simulation

Mechanical ventilation systems have acquired relevance in the past years in order to guarantee the hygrothermal comfort and indoor air quality (IAQ) in highly retrofitted residential buildings. The optimization of control strategies could provide a solution to this existing trade-off between energy efficiency, hygrothermal comfort and IAQ. In this publication, we propose a co-simulation approach (using EnergyPlus and Modelica) and a mathematical approximation of the discomfort of the occupant (namely, quadratic for relative humidity and exponential for CO2), and apply them to a demand controlled ventilation (DCV) scheme. Results show that this approach provides around 10% energy savings, while improving the thermal comfort, without compromising the humidity comfort or the IAQ. Finally, the developed functions could allow the control schemes to adapt to different occupant preferences, showing potential for future work

Exhausting domains of the symmetrized bidisc

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.Comment: 6 page

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

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

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

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