Tracking nitrogen losses in a greenhouse crop rotation experiment in North China using the EU-Rotate_N simulation model

Vegetable production in China is associated with high inputs of nitrogen, posing a risk of losses to the environment. Organic matter mineralisation is a considerable source of nitrogen (N) which is hard to quantify. In a two-year greenhouse cucumber experiment with different N treatments in North China, non-observed pathways of the N cycle were estimated using the EU-Rotate_N simulation model. EU-Rotate_N was calibrated against crop dry matter and soil moisture data to predict crop N uptake, soil mineral N contents, N mineralisation and N loss. Crop N uptake (Modelling Efficiencies (ME) between 0.80 and 0.92) and soil mineral N contents in different soil layers (ME between 0.24 and 0.74) were satisfactorily simulated by the model for all N treatments except for the traditional N management. The model predicted high N mineralisation rates and N leaching losses, suggesting that previously published estimates of N leaching for these production systems strongly underestimated the mineralisation of N from organic matter

An axiomatic approach to default risk and model uncertainty in rating systems

In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default risk measures via monetary risk measures, families of related tail risk measures, and Choquet capacities. In a second step, we turn our focus on default risk measures, which are given as worst-case PDs and distorted PDs. The latter are frequently used in order to take into account model risk for the computation of capital requirements through risk-weighted assets (RWAs), as demanded by the Capital Requirement Regulation (CRR). In this context, we discuss the impact of different default risk measures and margins of conservatism on the amount of risk-weighted assets.Comment: References have been updated, typos have been corrected, final version to appear in Journal of Mathematical Economic

Decomposition of General Premium Principles into Risk and Deviation

Nendel M, Schmeck MD, Riedel F. Decomposition of General Premium Principles into Risk and Deviation. Center for Mathematical Economics Working Papers. Vol 638 aktual. Version July 2020. Bielefeld: Center for Mathematical Economics; 2020.In this paper, we provide an axiomatic approach to general premium principles giving rise to a decomposition into risk, as a generalization of the expected value, and deviation, as a generalization of the variance. We show that, for every premium principle, there exists a maximal risk measure capturing all risky components covered by the insurance prices. In a second step, we consider dual representations of convex risk measures consistent with the premium principle. In particular, we show that the convex conjugate of the aforementioned maximal risk measure coincides with the convex conjugate of the premium principle on the set of all finitely additive probability measures. In a last step, we consider insurance prices in the presence of a not neccesarily frictionless market, where insurance claims are traded. In this setup, we discuss premium principles that are consistent with hedging using securization products that are traded in the market.AMS 2010 Subject Classification: 91B30; 91G20; 46A2

Convergence of infinitesimal generators and stability of convex monotone semigroups

Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not rely on the theory of viscosity solutions but use a recent comparison principle which uniquely determines the semigroup via its $\Gamma$-generator defined on the Lipschitz set and therefore resembles the classical analogue from the linear case. The framework also allows for discretizations both in time and space and covers a variety of applications. This includes Euler schemes and Yosida-type approximations for upper envelopes of families of linear semigroups, stability results and finite-difference schemes for convex HJB equations, Freidlin-Wentzell-type results and Markov chain approximations for a class of stochastic optimal control problems and continuous-time Markov processes with uncertain transition probabilities

On Nonlinear Expectations and Markov Chains under Model Uncertainty

Nendel M. On Nonlinear Expectations and Markov Chains under Model Uncertainty. Center for Mathematical Economics Working Papers. Vol 628. Bielefeld: Center for Mathematical Economics; 2019.The aim of this work is to give an overview on nonlinear expectation and to relate them to other concepts that describe model uncertainty or imprecision in a probabilistic framework. We discuss imprecise versions of stochastic processes with a particular interest in imprecise Markov chains. First, we focus on basic properties and representations of nonlinear expectations with additional structural assumptions such as translation invariance or convexity. In a second step, we discuss how stochastic processes under nonlinear expectations can be constructed via primal and dual representations. We illustrate the concepts by means of imprecise Markov chains with a countable state space, and show how families of Markov chains give rise to imprecise versions of Markov chains. We discuss dual representations and differential equations related to the latter.AMS 2010 Subject Classification: 28E05; 60G20; 60J27; 60J3

Data classification and criteria catalogue for data requirements

Data requirements for calibration and validation of agro-ecosystem models were elaborated and a classification scheme for the suitability of experimental data for model testing and improvement has been developed. The scheme enables to evaluate datasets and to classify datasets upon their quality to be used in crop modelling

A Note on Stochastic Dominance and Compactness

Nendel M. A Note on Stochastic Dominance and Compactness. Center for Mathematical Economics Working Papers. Vol 623. Bielefeld: Center for Mathematical Economics; 2019.In this work, we discuss completeness for the lattice orders of first and second order stochastic dominance. The main results state that, both, first and second order stochastic dominance induce Dedekind super complete lattices, i.e. lattices in which every bounded nonempty subset has a countable subset with identical least upper bound and greatest lower bound. Moreover, we show that, if a suitably bounded set of probability measures is directed (e.g. a lattice), then the supremum and infimum w.r.t. first or second order stochastic dominance can be approximated by sequences in the weak topology or in the Wasserstein-1 topology, respectively. As a consequence, we are able to prove that a sublattice of probability measures is complete w.r.t. first order stochastic dominance or second order stochastic dominance and increasing convex order if and only if it is compact in the weak topology or in the Wasserstein-1 topology, respectively. This complements a set of characterizations of tightness and uniform integrability, which are discussed in a preliminary section.AMS 2010 Subject Classification: 60E15; 60B10; 06B2

Identifying Agricultural Landscape Types for Brandenburg, Germany using IACS Data

The increasing demand for agricultural commodities for food and energy purposes has led to intensified agricultural production. This trend may manifest in agricultural compositions and landscape configurations that can have mixed and adverse impacts on the provision of ecosystem services. We rely on the EU’s plot-based data from the Integrated Administration and Control System (IACS) to identify different types of agricultural landscapes and their spatial distribution in Brandenburg, Germany, a study region strongly characterised by intensification trends. Based on a set of landscape metrics, we are able to characterise agricultural land use and identify six types of agricultural landscapes. We rely on a two-step cluster analysis for a hexagonal grid and find that agricultural land is dominated by cropland with different degrees of fragmentation. By providing a framework using landscape metrics derived from IACS data, our approach involves clustering to identify typologies that are transferable to other regions within the EU based on existing data. This framework can offer more tailored environmental and agricultural planning based on sophisticated measures that take into account local and regional characteristics