Stochastic Risk Model Research Articles

Variation in the effect of carcass decontamination impacts the risk for consumers

To enhance food safety, whole carcass decontamination during slaughter has been considered as a control measure to reduce pathogen concentrations on meat. The effect of such decontamination is usually measured in terms of the mean log reduction in concentration. However, the variation in this reduction may also contribute to the overall impact of the decontamination measure. Therefore, this study focuses on the relative contribution of mean and variation for the effect of decontamination in the slaughter-line expressed in terms of the effect on human health risk.A stochastic risk model is developed to assess the potential effects of pig carcass decontamination at the end of slaughter on the risk of salmonellosis for Danish consumers. Salmonella concentrations are represented by a lognormal distribution fitted to microbiological data, characteristic for Salmonella numbers on carcasses at the end-point of Danish slaughterhouses. Decontamination scenarios are represented by various gamma distributions with different means and standard deviations. The values chosen for these parameters are based on experimental data of the effect of real decontamination procedures applied to pork.Results show that the variation of decontamination has a relevant effect on risk reduction for the consumer: the higher the variation, the lower the overall risk reduction. This effect is particularly evident for procedures with a lower mean reduction (≤2.5 log10), but less so for highly efficient decontamination procedures (>2.5 log10 mean reduction). This difference is affected by the initial level of carcass contamination with Salmonella. With increasing mean and standard deviation of initial bacterial concentrations, it becomes increasingly relevant to account for the variation of the decontamination action, even if the mean decontamination effect is high.We conclude that for decontamination procedures with an overall mean reduction effect of 1–2 log10, it is important to consider the variation in effect: if the variation is large, the final effect of decontamination can be considerably smaller than expected on the basis of the mean only and efforts should be put in place to reduce the variation of the procedure. However, when a treatment of high mean reduction (>2.5 log10) is used, the impact of variation becomes smaller and may be negligible.

Risk-based testing of imported animals: A case study for bovine tuberculosis in The Netherlands

In intra-EU trade, the health status of animals is warranted by issuing a health certificate after clinical inspection in the exporting country. This certificate cannot provide guarantee of absence of infection, especially not for diseases with a long incubation period and no overt clinical signs such as bovine tuberculosis (bTB). The Netherlands are officially free from bTB since 1999. However, frequent reintroductions occurred in the past 15 years through importation of infected cattle. Additional testing (AT) of imported cattle could enhance the probability of detecting an imported bTB infection in an early stage. The goal of this study was to evaluate the effectiveness of risk-based AT for bTB in cattle imported into The Netherlands.A generic stochastic import risk model was developed that simulates introduction of infection into an importing country through importation of live animals. Main output parameters are the number of infected animals that is imported (Ninf), the number of infected animals that is detected by testing (Ndet), and the economic losses incurred by importing infected animals (loss). The model was parameterized for bTB. Model calculations were optimized to either maximize Ndet or to minimize loss.Model results indicate that the risk of bTB introduction into The Netherlands is very high. For the current situation in which Dutch health checks on imported cattle are limited to a clinical inspection of a random sample of 5–10% of imported animals, the calculated annual Ninf=99 (median value). Random AT of 8% of all imported cattle results in Ndet=7 (median value), while the median Ndet=75 if the sampling strategy for AT is optimized to maximize Ndet. However, in the latter scenario, loss is more than twice as large as in the current situation, because only calves are tested for which cost of detection is higher than the expected gain of preventing a possible outbreak. When optimizing the sampling strategy for AT to minimize loss, only breeding and production cattle are selected for AT resulting in Ndet=1 (median value). Loss is; however, reduced by 75% if compared to the current situation.We conclude that the effectiveness of AT can greatly be improved by risk-based sampling. The optimal sampling strategy for risk-based AT for bTB is highly dependent on the objective of AT. If economic losses are to be contained, AT should focus on breeding and production cattle originating from high-risk countries.

Investigation of the food value chain of ready-to-eat chicken and the associated risk for staphylococcal food poisoning in Tshwane Metropole, South Africa

The objective of the study was to better understand the informal markets for ready-to-eat (RTE) chicken in Tshwane Metropole, Gauteng Province, South Africa, and in particular the links between the formal and informal sector. As part of this, we assessed the risk of a common food poisoning (staphylococcal) through consumption of RTE chicken sold by informal vendors. We used participatory risk assessment, a novel approach to understanding food safety in data scarce environments to collect information. Structured interviews and focus group discussions with informal vendors (n = 237) were conducted to understand poultry value chains for informal RTE chicken, business operation and hygiene practices. Samples (n = 100) of RTE were collected from informal vendors in six major taxi ranks. Staphylococcus aureus counts were determined using 3M™ Petrifilm™ plates. Data collected in this present study plus information obtained from reviewing of literature, were used to develop a stochastic risk model. The number of colonies which were too numerous to count (TNTC) was artificially modeled. A mapping of the informal food value chain revealed that there are four possible value chains and that chicken spilled over from formal to informal markets. The prevalence of S. aureus in RTE chicken samples (44%; 90% CI: 36.1%–52.2%) was high. The mean S. aureus counts in the ready to eat chicken was 103.6 (90%CI: 103.3–103.9), and the risk of purchasing chicken of unsatisfactory quality (>103 cfu/g) was 32.9% (90%CI: 25.5%–40.4%). The probability of food poisoning due to consumption of RTE chicken contaminated with staphylococcal enterotoxin was estimated to be 1.3% (90% CI: 0%–2.7%). Sensitivity analysis showed that the probability of S. aureus having the enterotoxin gene was the most sensitive parameter for food poisoning. This was followed by S. aureus concentration in RTE chicken and lastly the prevalence of S. aureus in ready-to-eat chicken. This study demonstrates the existence of a strong link between formal and the informal market. In view of the low risk observed, the relevant authorities in Tshwane should continue to support the informal sale of RTE chicken. However, there is still a need for provision of hygiene training to reduce the concentration levels of S. aureus on the RTE chicken, and to promote the sale of safer affordable source of protein for the large urban poor population in South Africa. This will also help secure the opportunities for employment associated with the trade.

Ruin probabilities for an insurance company based on some stochastic risk models

The paper is concerned with a stochastic risk model with independent random claims and premiums. Recurrence formulas for the ruin probabilities of an insurance company at times of claim payments are obtained. Both the random premiums and the insurance damages are assumed to be independent and identically distributed. The number of claims and premiums are independent Poisson processes, both of which are independent of the size of premiums and claims. We consider the case when the random premiums and insurance damages are exponentially distributed and the more general case when they are gamma distributed with integer parameters. Based on the probabilities obtained in this paper, it is possible to calculate the ruin probabilities on infinite and finite time intervals. Examples are given.

Sensitivity Analysis for Critical Control Points Determination and Uncertainty Analysis to Link FSO and Process Criteria: Application to Listeria monocytogenes in Soft Cheese Made from Pasteurized Milk

Microbiological food safety is an important economic and health issue in the context of globalization and presents food business operators with new challenges in providing safe foods. The hazard analysis and critical control point approach involve identifying the main steps in food processing and the physical and chemical parameters that have an impact on the safety of foods. In the risk-based approach, as defined in the Codex Alimentarius, controlling these parameters in such a way that the final products meet a food safety objective (FSO), fixed by the competent authorities, is a big challenge and of great interest to the food business operators. Process risk models, issued from the quantitative microbiological risk assessment framework, provide useful tools in this respect. We propose a methodology, called multivariate factor mapping (MFM), for establishing a link between process parameters and compliance with a FSO. For a stochastic and dynamic process risk model of Listeriamonocytogenes in soft cheese made from pasteurized milk with many uncertain inputs, multivariate sensitivity analysis and MFM are combined to (i) identify the critical control points (CCPs) for L.monocytogenes throughout the food chain and (ii) compute the critical limits of the most influential process parameters, located at the CCPs, with regard to the specific process implemented in the model. Due to certain forms of interaction among parameters, the results show some new possibilities for the management of microbiological hazards when a FSO is specified.

Ordering of multivariate risk models with respect to extreme portfolio losses

Abstract The notion of asymptotic portfolio loss order is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of spectral measures. This allows for analytical and numerical verification in applications. Worst and best case dependence structures with respect to the asymptotic portfolio loss order are determined. Comparison criteria in terms of further stochastic ordering notions are derived. The examples include elliptical distributions and multivariate regularly varying models with Gumbel, Archimedean, and Galambos copulas. Particular interest is paid to the inverse influence of dependence on the diversification of risks with infinite expectations.

Risk assessment of staphylococcal poisoning due to consumption of informally-marketed milk and home-made yoghurt in Debre Zeit, Ethiopia

The objectives of the study were twofold: to prove that participatory risk assessment can be applied to informally-marketed foods, and to assess the risk of staphylococcal poisoning through consumption of raw milk and home-made yoghurt in Debre Zeit, Ethiopia. Rapid urban appraisals were combined with conventional interviews to identify and quantify formal and informal milk value chains and to collect information on consumers' food preparation and consumption behavior. Milk was sampled in 170 dairy farms and 5 milk collection centers and microbiological tests were conducted. Published data on milk fermentation in Ethiopia was combined with a growth model of Staphylococcus aureus to develop a stochastic risk model. The annual incidence rate of staphylococcal poisoning was estimated to be 20.0 (90% CI: 13.9-26.9) per 1000 people. When the effect of fermentation was removed from the model, the annual incidence rate increased to 315.8 (90% CI: 224.3-422.9) per 1000 people, showing the importance of traditional food preparation methods in risk mitigation; traditional milk fermentation reduced the risk by 93.7%. Improving the safety of milk and dairy products could be achieved through supporting appropriate traditional food preparation and consumption where an industrial risk mitigation system is not feasible. Participatory risk assessment was shown to be applicable to informal food value chain.

Water reclamation redesign for reducing Cryptosporidium risks at a recreational spray park using stochastic models

Recreational outbreaks associated with sprayparks are well recognized, and may be partly due to the engineering designs used for their water reclamation systems are problematic to control. This work is based on an outbreak of cryptosporidiosis linked to a spraypark in New York State, where it was determined, specifically that the spraypad (the main attraction) was the primary exposure point. We first determined the likely dose the spraypad users were exposed to, then modeled the efficacy of the treatment system and used this to inform a Monte Carlo method to estimate the probability of infection and illness for the users of the spraypad. The current treatment system which consists of; two holding tanks, a dual media filter and chlorine injection as well as two design change recommendations were modeled using three independent Markov chain models. Within the current treatment system design the receiving tank for the treatment train is also connected with a second pipe to the spraypad used to deliver the return (treated) water, this return pipe is acting potentially as a bypass for the treatment train. Based on the risk assessments performed it is recommended that the bypass pipe be removed from the treatment system since in doing so the probability of infection and illness were reduced appreciably. Secondarily including an ozone contactor was shown to slightly reduce the risk further and provide a multiple barrier.

From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital

In this paper we raise the matter of considering a stochastic model of the surrender rate instead of the classical S-shaped deterministic curve (in function of the spread), still used in almost all insurance companies. For extreme scenarios, due to the lack of data, it could be tempting to assume that surrenders are conditionally independent with respect to a S-curve disturbance. However, we explain why this conditional independence between policyholders decisions, which has the advantage to be the simplest assumption, looks particularly maladaptive when the spread increases. Indeed the correlation between policyholders decisions is most likely to increase in this situation. We suggest and develop a simple model which integrates those phenomena. With stochastic orders it is possible to compare it to the conditional independence approach qualitatively. In a partially internal Solvency II model, we quantify the impact of the correlation phenomenon on a real life portfolio for a global risk management strategy.

Time-Varying Asset Volatility and the Credit Spread Puzzle

Structural credit risk models have faced difficulties in matching observed market credit spreads while simultaneously matching default rates, recoveries, leverage and risk premia - a shortcoming that has become known as the credit spread puzzle. We ask whether stochastic asset volatility, as an extension to this model class, has the ability to help resolve this puzzle. We identify that although there are three ways in which uncertainty about asset risk can influence spreads (asset risk volatility itself, dependence between the levels of risk and asset value and finally volatility risk premia), in a calibration setting only the volatility risk premium channel is economically significant. We show that this feature of a stochastic asset risk model allows it to match historical spreads and equity volatility as well. We also provide estimates of the required variance risk premia.

Stochastic Modelling – Boon or Bane for Insurance Industry Capital Regulation?

Regulation of the financial industry should pursue three key objectives: consumer protection, market stability, and competitive efficiency. This article discusses core elements of a capital regime that could be used to develop regulation that meets these objectives while fostering an industry-wide enhancement of risk management. The authors argue that a pre-commitment approach can have considerable advantages over regulation based on (stochastic) risk models, as the latter can have adverse effects, especially on market stability and competitive efficiency, while consumer protection would have to be supplemented by additional requirements (such as scenario tests) in any case. Academic studies on capital regulation based on stochastic models have focused more on banking and less on insurance, while work by insurance practitioners has concentrated on the implications for management. The authors, therefore, wish to contribute to a more fundamental discussion of the design of capital and risk management regulation of the insurance industry.

Where should the effort be put to reduce the Salmonella prevalence in the slaughtered swine carcass effectively?

Infection with Salmonella Typhimurium is seldom associated with clinical disease in pigs. However, control is important as the public is concerned about the human health impact. The producers, the abattoirs and the authorities are interested in implementing procedures to mitigate this risk. To evaluate the effect of different procedures, a stochastic risk model was developed to simulate the prevalence of Salmonella infection during the production process from the live pig on the farm, to the final carcass. This paper describes the model and findings of simulating different control scenarios. The variables with maximum effect on the Salmonella prevalence on the final carcass were (1) number of herds with a high prevalence of Salmonella, (2) singeing efficiency, (3) contamination and cross-contamination at degutting and (4) cross-contamination during handling. However, improvement of any single factor in isolation had a limited impact upon the level of contamination. The largest reduction was observed when several factors were improved concurrently.

Flood risk assessment and associated uncertainty

Abstract. Flood disaster mitigation strategies should be based on a comprehensive assessment of the flood risk combined with a thorough investigation of the uncertainties associated with the risk assessment procedure. Within the "German Research Network of Natural Disasters" (DFNK) the working group "Flood Risk Analysis" investigated the flood process chain from precipitation, runoff generation and concentration in the catchment, flood routing in the river network, possible failure of flood protection measures, inundation to economic damage. The working group represented each of these processes by deterministic, spatially distributed models at different scales. While these models provide the necessary understanding of the flood process chain, they are not suitable for risk and uncertainty analyses due to their complex nature and high CPU-time demand. We have therefore developed a stochastic flood risk model consisting of simplified model components associated with the components of the process chain. We parameterised these model components based on the results of the complex deterministic models and used them for the risk and uncertainty analysis in a Monte Carlo framework. The Monte Carlo framework is hierarchically structured in two layers representing two different sources of uncertainty, aleatory uncertainty (due to natural and anthropogenic variability) and epistemic uncertainty (due to incomplete knowledge of the system). The model allows us to calculate probabilities of occurrence for events of different magnitudes along with the expected economic damage in a target area in the first layer of the Monte Carlo framework, i.e. to assess the economic risks, and to derive uncertainty bounds associated with these risks in the second layer. It is also possible to identify the contributions of individual sources of uncertainty to the overall uncertainty. It could be shown that the uncertainty caused by epistemic sources significantly alters the results obtained with aleatory uncertainty alone. The model was applied to reaches of the river Rhine downstream of Cologne.

An empirical reassessment of target-zone nonlinearities

In this paper we investigate the presence of target-zone nonlinearities in the Pound Sterling/German Mark exchange rate for the period of the UK European Exchange Rate Mechanism (ERM) membership using data with frequency of every 2 days. Tests against general nonlinear specifications as well as specifications consistent with a stochastic devaluation risk model of exchange rate target zones are carried out using recursive techniques. In addition, the significance of nonlinear effects is analysed within a recursive Bayesian framework. We find evidence of target-zone nonlinearities in the whole sample but the recursive analysis yields support for the presence of such nonlinearities only in specific subsamples. Our results imply that the reduction in the UK inflation rate was most likely a consequence of contractionary policies rather than of the expectational effects associated with the target zone.