Noy-Meir's simple but insightful model of grazing-system dynamics was used to draw broader inferences from empirical data generated by a 17-year field trial with beef cattle grazing a Mediterranean grassland in northern Israel. After calibration of its parameters against the field results, the model predictions were tested against an independent set of data obtained from the study site; they were within acceptable deviations from the inherently noisy field data. The calibrated model was used to analyse the effects of changes to two key grazing-management factors – stocking density and early-season grazing deferment – on biomass dynamics and forage consumption. The simulated results were used to calculate forage deficits and supplementary feed requirements for optimum herd performance during the growth (‘green’) season and throughout the year. The results revealed a critical stocking density of 0.7 Animal Units (AU)/ha, above which early-season deferment reduced the amount of supplementary feed required to maintain the optimum production of the herd. Optimum stocking is higher when the grassland is used mainly in the highly nutritious green season. Responses of the strongly seasonal Mediterranean grassland to the interaction between stocking density and early-season grazing deferment were expressed by a calibrated model, in terms that determine the efficiency of forage supplementation of the herd during the green season and throughout the year.

Validation of risk models is required by regulators and demanded by management and shareholders. Those models rely in practice heavily on Monte Carlo (MC) simulations. Given their complexity, the convergence of the MC algorithm is difficult to prove mathematically. To circumvent this problem and nevertheless explore the conditions of convergence, we suggest an analytical approach. Considering standard models, we compute, via mixing techniques, closed form formulas for risk measures as Value-at-Risk (VaR) VaR or Tail Value-at-Risk (TVaR) TVaR on a portfolio of risks, and consequently for the associated diversification benefit. The numerical convergence of MC simulations of those various quantities is then tested against their analytical evaluations. The speed of convergence appears to depend on the fatness of the tail of the marginal distributions; the higher the tail index, the faster the convergence. We also explore the behaviour of the diversification benefit with various dependence structures and marginals (heavy and light tails). As expected, it varies heavily with the type of dependence between aggregated risks. The diversification benefit is also studied as a function of the risk measure, VaR or TVaR.

Predicting the off-target movement of agrochemicals applied to turf is an essential component for assessing risk to aquatic environments. For surface transport, a fully validated model does not exist. Such a model is required to make cost effective risk assessments and regulatory evaluations. To address this deficiency, a turf model validation program is outlined in this paper. The effect of turf characteristics on the fate and movement of pesticides is presented followed by the discussion of the selection for a proper turf runoff model. The design and implementation of small plot runoff studies and their usefulness in model validation are discussed. The procedures of model calibration and model verification are explained for model validation purpose.

Do quasi-physically based models with more detail perform better than regression or other empirical models? This is a question that was raised many years ago and still remains. In an effort to respond to this question, the author reviews the needs and concerns of users and then divides the large number of models into three classes: (1) screening, (2) research, and (3) planning, monitoring, and assessment. Empirical and causal (physically based) models are contrasted and the advantages and disadvantages of each described. Sources of model uncertainty (properties of data bases, model structure, parameter estimation methods, algorithmic implementation, verification and validation, and future users) that lead to skepticism about models' performance are investigated. Simulation scale and spatial variability are also important considerations. The leading question is then discussed from the perspective of screening, research, and planning, monitoring, and regulatory models.

The ability of the pesticide root zone model (PRZM) and the groundwater-loading effects of agricultural management systems (GLEAMS) model to predict movement of two herbicides in soil was evaluated using site-specific environmental data from sites in three states. Predictions of herbicide movement with site-specific data were compared to predictions using more generalized database soil and pesticide data within each model. Field experiments examined fluometuron and norflurazon movement in three soils representative of the cotton-growing regions of the southeastern United States. In comparing the use of site-specific vs. database values, the small increase in accuracy using site-specific inputs would not justify the large cost to obtain the data. The databases for each model gave predictions similar to those using the site-specific numbers. Both the PRZM and the GLEAMS model had similar accuracy levels in predicting the presence of fluometuron or norflurazon present in three surface soils, although each model tended to overpredict movement and total herbicide concentration, especially at lower herbicide concentrations. At higher herbicide concentrations, prediction accuracy was less than that probably needed to predict agronomically relevant herbicide concentrations in surface soils.

The local volatility model is a well-known extension of the Black–Scholes constant volatility model, whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide range of implied volatility surfaces. The model is easy to calibrate and still very popular in foreign exchange option trading. In this paper, we address a question of validation of the local volatility model. Different stochastic models for the underlying asset can be calibrated to provide a good fit to the current market data, which should be recalibrated every trading date. A good fit to the current market data does not imply that the model is appropriate, and historical backtesting should be performed for validation purposes. We study delta hedging errors under the local volatility model using historical data from 2005 to 2011 for the AUD/USD implied volatility. We performed backtests for a range of option maturities and strikes using sticky delta and theoretically correct delta hedging. The results show that delta hedging errors under the standard Black–Scholes model are no worse than those of the local volatility model. Moreover, for the case of in- and at-the-money options, the hedging error for the Black–Scholes model is significantly better.

The relationship of the chain ladder method to mathematical statistics has long been debated in actuarial science. During the 1990s it became clear that the originally deterministic chain ladder can be seen as an autoregressive time series or as a multiplicative Poisson model. This paper draws on recent research and concludes that chain ladder can be seen as a structured histogram. This gives a direct link between classical aggregate methods and continuous granular methods. When the histogram is replaced by a smooth counterpart, we have a continuous chain ladder model. Re-inventing classical chain ladder via double chain ladder and its extensions introduces statistically solid approaches of combining paid and incurred data with direct link to granular data approaches. This paper goes through some of the extensions of double chain ladder and introduces new approaches to incorporating and modelling incurred data.

A benchmark is organised to quantify the variability relative to structure dynamicscomputations. The chosen demonstrator is a pump in service in thermal central units, whichis an engineered system with not well-known parameters, considered in its workenvironment. The blind modal characterisation of the separate pump components shows a5%–12% variability on eigenfrequency values and a less than 15% frequency error incomparison with experimental values. The numerical-experimental MAC numbers reach 0.7 atthe maximum, even after updating. An example of modal results on the pump assembly fixedis presented, which shows a larger discrepancy with measurement values, essentially due tothe modelling of the interfaces and boundary condition, and to the possible simplificationof the main components F.E. models to reduce their size. Though a significant frequencyerror, the first overall modes are correctly identified. If this tendency can be confirmedfrom all the participants’ results, the conclusion to be drawn is that, if the predictivecapability of F.E. models to represent the dynamical behaviour of sub-structures issatisfactory, the one relative to structures that are built-up of several components doesnot allow their confident use. Additional information issued from measurements is neededto improve their accuracy.