Portfolio Insurance and model uncertainty

Some real-world insurance products contain a minimum-wealth or an income-stream guarantee, both of which have to be met irrespective of capital market conditions. Therefore, sellers of such products are well advised to pursue a portfolio strategy that can meet these minimum investment goals if they want to avoid additional cash payments. Portfolio Insurance seems to be the solution to this portfolio problem. However, this paper shows that Portfolio Insurance cannot protect minimum investment goals because its strategies are fitted to a particular form of market risk. Decision makers do not know for sure (with probability one) what the true form of market risk is (model uncertainty); thus model uncertainty makes Portfolio Insurance fail. RID="*" ID="*" I thank two anonymous referees and the participants of the “3rd Passauer Finanzwerkstatt”, in particular Ariane Rei? and Thomas Braun, for their valuable comments. In addition, special thanks goes to Alexander Kempf, whose suggestions have significantly improved the paper.     

Multivariate receptor models and model uncertainty

Estimation of the number of major pollution sources, the source composition profiles, and the source contributions are the main interests in multivariate receptor modeling. Due to lack of identifiability of the receptor model, however, the estimation cannot be done without some additional assumptions.

A common approach to this problem is to estimate the number of sources, q, at the first stage, and then estimate source profiles and contributions at the second stage, given additional constraints (identifiability conditions) to prevent source rotation/transformation and the assumption that the q-source model is correct. These assumptions on the parameters (the number of sources and identifiability conditions) are the main source of model uncertainty in multivariate receptor modeling.

In this paper, we suggest a Bayesian approach to deal with model uncertainties in multivariate receptor models by using Markov chain Monte Carlo (MCMC) schemes. Specifically, we suggest a method which can simultaneously estimate parameters (compositions and contributions), parameter uncertainties, and model uncertainties (number of sources and identifiability conditions). Simulation results and an application to air pollution data are presented.     

Model validation under epistemic uncertainty

This paper develops a methodology to assess the validity of computational models when some quantities may be affected by epistemic uncertainty. Three types of epistemic uncertainty regarding input random variables - interval data, sparse point data, and probability distributions with parameter uncertainty - are considered. When the model inputs are described using sparse point data and/or interval data, a likelihood-based methodology is used to represent these variables as probability distributions. Two approaches - a parametric approach and a non-parametric approach - are pursued for this purpose. While the parametric approach leads to a family of distributions due to distribution parameter uncertainty, the principles of conditional probability and total probability can be used to integrate the family of distributions into a single distribution. The non-parametric approach directly yields a single probability distribution. The probabilistic model predictions are compared against experimental observations, which may again be point data or interval data. A generalized likelihood function is constructed for Bayesian updating, and the posterior distribution of the model output is estimated. The Bayes factor metric is extended to assess the validity of the model under both aleatory and epistemic uncertainty and to estimate the confidence in the model prediction. The proposed method is illustrated using a numerical example.     

Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation

International Journal of Mechanics and Materials in Design - The traditional ellipsoid convex set is a kind of basic non-probabilistic model to measure uncertainties. However, it is difficult or...     

The uncertainty of parallel model coordinate measuring machine

The Stewart platform is one of 6-DOF (6 degrees of freedom) parallel mechanism. A parallel mechanism is a mechanism to connect six actuators in parallel between the base and the stage. It is necessary to calibrate the kinematic parameters that compose the mechanism in order to use the parallel mechanism as the coordinate measuring machine. Additionally, it is necessary to estimate the uncertainty about the measurement results. In this study, the kinematics parameters are estimated by using the calibration point in one point, the uncertainty is estimated at several measurement coordinates from kinematic parameters and postures angle. The verification method is shown following; i) The amount of the actuator expansion and contraction in the parallel mechanism is assumed to be a value obtained with the sensor and, the kinematic parameters are estimated from the values by using the least squares method. ii)The coordinates of the stylus are calculated from the estimated kinematic parameters by forward kinematics. The uncertainty is estimated from the coordinates of the stylus. As a result, the influence of the uncertainty is reported when the target coordinates are measured.     

Models and model uncertainty in the context of risk analysis

This paper addresses the concept of model uncertainty within the context of risk analysis. Though model uncertainty is a topic widely discussed in the risk analysis literature, no consensus seems to exist on its meaning, how it should be measured, or its impact on the application of analysis results in decision processes. The purpose of this paper is to contribute to clarification. The first parts of the paper look into the contents of the two terms ‘model’ and ‘uncertainty’. On this platform it is discussed how focus on model uncertainty merely leads to muddling up the message of the analysis, if risk is interpreted as a true, inherent property of the system, to be estimated in the risk analysis. An alternative approach is to see the models as means for expressing uncertainty regarding the system performance. In this case, it is argued, the term ‘model uncertainty’ loses its meaning.     

Industrial fire simulation and uncertainty associated with the Emission Dispersion Model

The use of numerical modeling in the field of industrial fire accidentology has become common nowadays and this tendency is expected to increase with the development of performance simulation tools. Despite the constant development of fire modeling tools, the current state of the art is not yet able to accurately predict fire phenomena. This gap between the reality and simulations is probably due to the presence of some level of uncertainty, which may occur from the meteorological inputs, diffusion assumptions, plume dynamics, or emission production. To cope with the presence of uncertainties in the input data, we propose an uncertainty analysis enabling to avoid as much as possible bad decisions that may have a large impact in domains such as safety. In this study, we are interested in the uncertainty propagation related to NO₂ atmospheric dispersion resulting from a crude oil tank fire. Uncertainties were defined a priori for each of the following input parameters: wind speed, NO₂ emission rate, and viscosity and diffusivity coefficients. For that purpose, a Monte Carlo approach has been used. In order to evaluate the importance of the considered parameters on the NO₂ dispersion, new sensitivity indicator has been developed. The obtained results showed that the viscosity coefficient and the wind speed are the most significant input parameters with respect to NO₂ concentration near to the source of fire, while the wind speed and the initial concentration are the important parameters for distant areas.     

Development of a production inventory model with uncertainty and reliability considerations

This paper addresses a problem of an imperfect production system under fuzzy demand and inventory holding cost. Production process reliability is considered because of the imperfect production process. In this problem, reliability of the system in regards to producing defective and non-defective items is considered as a decision variable. The objective is to maximize the graded mean integration value (GMIV) of the expected average profit while considering revenues as well as any other relevant costs. The developed model belongs to the class of a geometric programming. We have developed a simple mathematical methodology to solve the model. Genetic algorithm and simulated annealing algorithms are also applied to solve and validate the results. A numerical example has been presented to interpret the solutions.     

Bayesian risk-based decision method for model validation under uncertainty

This paper develops a decision-making methodology for computational model validation, considering the risk of using the current model, data support for the current model, and cost of acquiring new information to improve the model. A Bayesian decision theory-based method is developed for this purpose, using a likelihood ratio as the validation metric for model assessment. An expected risk or cost function is defined as a function of the decision costs, and the likelihood and prior of each hypothesis. The risk is minimized through correctly assigning experimental data to two decision regions based on the comparison of the likelihood ratio with a decision threshold. A Bayesian validation metric is derived based on the risk minimization criterion. Two types of validation tests are considered: pass/fail tests and system response value measurement tests. The methodology is illustrated for the validation of reliability prediction models in a tension bar and an engine blade subjected to high cycle fatigue. The proposed method can effectively integrate optimal experimental design into model validation to simultaneously reduce the cost and improve the accuracy of reliability model assessment.     

Information inaccuracy in inventory systems: stock loss and stockout

Many companies have automated their inventory management processes and now rely on information systems when making critical decisions. However, if the information is inaccurate, the ability of the system to provide a high availability of products at the minimal operating cost can be compromised. In this paper, analytical and simulation modelling demonstrate that even a small rate of stock loss undetected by the information system can lead to inventory inaccuracy that disrupts the replenishment process and creates severe out-of-stock situations. In fact, revenue losses due to out-of-stock situations can far outweigh the stock losses themselves. This sensitivity of the performance to the inventory inaccuracy becomes even greater in systems operating in lean environments. Motivated by an automatic product identification technology under development at the Auto-ID Center at MIT, various methods of compensating for the inventory inaccuracy are presented and evaluated. Comparisons of the methods reveal that the inventory inaccuracy problem can be effectively treated even without automatic product identification technologies in some situations.     

A robust optimisation model for production planning and pricing under demand uncertainty

The profitability of every manufacturing plant is dependent on its pricing strategy and a production plan to support the customers’ demand. In this paper, a new robust multi-product and multi-period model for planning and pricing is proposed. The demand is considered to be uncertain and price-dependent. Thus, for each price, a range of demands is possible. The unsatisfied demand is considered to be lost and hence, no backlogging is allowed. The objective is to maximise the profit over the planning horizon, which consists of a finite number of periods. To solve the proposed model, a modified unconscious search (US) algorithm is introduced. Several artificial test problems along with a real case implementation of the model in a textile manufacturing plant are used to show the applicability of the model and effectiveness of the US for tackling this problem. The results show that the proposed model can improve the profitability of the plant and the US is able to find high quality solutions in a very short time compared to exact methods.     

The effect of model uncertainty on cooperation in sensorimotor interactions

Decision-makers have been shown to rely on probabilistic models for perception and action. However, these models can be incorrect or partially wrong in which case the decision-maker has to cope with model uncertainty. Model uncertainty has recently also been shown to be an important determinant of sensorimotor behaviour in humans that can lead to risk-sensitive deviations from Bayes optimal behaviour towards worst-case or best-case outcomes. Here, we investigate the effect of model uncertainty on cooperation in sensorimotor interactions similar to the stag-hunt game, where players develop models about the other player and decide between a pay-off-dominant cooperative solution and a risk-dominant, non-cooperative solution. In simulations, we show that players who allow for optimistic deviations from their opponent model are much more likely to converge to cooperative outcomes. We also implemented this agent model in a virtual reality environment, and let human subjects play against a virtual player. In this game, subjects'' pay-offs were experienced as forces opposing their movements. During the experiment, we manipulated the risk sensitivity of the computer player and observed human responses. We found not only that humans adaptively changed their level of cooperation depending on the risk sensitivity of the computer player but also that their initial play exhibited characteristic risk-sensitive biases. Our results suggest that model uncertainty is an important determinant of cooperation in two-player sensorimotor interactions.     

A bi-objective robust model for emergency resource allocation under uncertainty

Emergency resource allocation constitutes one of the most critical elements of response operations in the field of emergency management. This paper addresses an emergency resource allocation problem which involves multiple competing affected areas and one relief resource centre under supply shortage and uncertainty in the post-disaster phase. In humanitarian situations, both the efficiency and fairness of an allocation policy have a considerable influence on the effectiveness of emergency response operations. Thus, we formulate a bi-objective robust emergency resource allocation (BRERA) model which tries to maximise efficiency as well as fairness under different sources of uncertainties. To obtain decision-makers’ most preferred allocation policy, we propose a novel emergency resource allocation decision method which consists of three steps: (1) develop a bi-objective heuristic particle swarm optimisation algorithm to search the Pareto frontier of the BRERA model; (2) select a coefficient to measure fairness; and (3) establish a decision method based on decision-makers’ preference restricted by the fairness coefficient. Finally, a real case study taken from the 5 December 2008 Wenchuan Earthquake demonstrates the effectiveness of the proposed method through numerical results. The solution and model robustness are also analysed.     

A mathematical model for vehicle routing problem under endogenous uncertainty

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.     

A three-stage model for closed-loop supply chain configuration under uncertainty

In this paper, a general closed-loop supply chain (CLSC) network is configured which consists of multiple customers, parts, products, suppliers, remanufacturing subcontractors, and refurbishing sites. We propose a three-stage model including evaluation, network configuration, and selection and order allocation. In the first stage, suppliers, remanufacturing subcontractors, and refurbishing sites are evaluated based on a new quality function deployment (QFD) model. The proposed QFD model determines the relationship between customer requirements, part requirements, and process requirements. In addition, the fuzzy sets theory is utilised to overcome the uncertainty in the decision-making process. In the second stage, the closed-loop supply chain network is configured by a stochastic mixed-integer nonlinear programming model. It is supposed that demand is an uncertain parameter. Finally in the third stage, suppliers, remanufacturing subcontractors, and refurbishing sites are selected and order allocation is determined. To this end, a multi-objective mixed-integer linear programming model is presented. An illustrative example is conducted to show the process. The main novel innovation of the proposed model is to consider the CLSC network configuration and selection process simultaneously, under uncertain demand and in an uncertain decision-making environment.     

Basic binary state-space model for time-varying communication channels: uncertainty and information capacity

This paper looks at capacity achieving detection strategies for information transfer over time-varying channels. The time-varying binary symmetric channel (TV-BSC) is identified as the basic binary state-space model. Separation of entropies principles and the TV-BSC model-based state-space approach are used to determine the performance bounds for coherent and non-coherent detection over time-varying communication channels. The mutual information rate over the TV-BSC, assuming channel estimation in the presence of channel noise, is shown to be below the channel information capacity because of lack of perfect channel knowledge. Furthermore, it is shown that TV-BSC model-based differential detection has a fundamental advantage over the channel estimation based detection since it theoretically preserves the TV-BSC information capacity when the observation interval approaches infinity. Simulation analysis corroborates the theoretical results, showing that multiple-symbol differential detection practically achieves the TV-BSC capacity in just a few symbol observation times.     

Variability and uncertainty of biokinetic model parameters: the discrete empirical Bayes approximation

In the Bayesian approach to internal dosimetry, uncertainty and variability of biokinetic model parameters need to be taken into account. The discrete empirical Bayes approximation replaces integration over biokinetic model parameters by discrete summation in the evaluation of Bayesian posterior averages using Bayes theorem. The discrete choices of parameters are taken as best-fit point determinations of model parameters for a study subpopulation with extensive data. A simple heuristic model is constructed to numerically and theoretically study this approximation. The heuristic example is the measurement of heights of a group of people, say from a photograph where measurement uncertainty is significant. A comparison is made of posterior mean and standard deviation of height after a measurement, (i) using the exact prior describing the distribution of true height in the population and (ii) using the approximate discrete empirical Bayes prior obtained from measurements of some study subpopulation.     

An optimization model for a crop deficit irrigation system under uncertainty

In this study, an inexact nonlinear programming model under uncertainty is developed by incorporating a water production function into the crop irrigation system optimization framework. By introducing a time parameter, this model can address the uncertainty associated with the irrigation schedule for different crops and their planting stages. The developed model was applied to a case study of an agricultural water resources management problem to demonstrate its applicability. Through scenario analysis under different precipitation levels, the key planting stage of crops and the amount of water for the irrigation schedule that could significantly affect system benefits were identified. By using intervals to represent uncertain parameters, more reliable and practical decision alternatives were generated through the presented model in typical hydrological years (i.e. wet, normal and dry years).