Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations.

To support decision-makers considering adopting integrated pest management (IPM) cropping in Norway, we used stochastic efficiency analysis to compare the risk efficiency of IPM cropping and conventional cropping, using data from a long-term field experiment in southeastern Norway, along with data on recent prices, costs, and subsidies. Initial results were not definitive, so we applied stochastic efficiency with respect to a function, limiting the assumed risk aversion of farmers to a plausible range. We found that, for farmers who are risk-indifferent to moderately (hardly) risk averse, the conventional system was, compared to IPM, less (equally) preferred.

In recent years, a growing number of capital market professionals have projected a low-return environment in US investment portfolios – where returns in most asset classes are expected to drop below historical rates. While these specific forecasts may not fully materialize, it is natural for cyclical investment markets to go through extended periods of lower returns, creating significant risks for public pension systems which rely on investment returns to sustain their long-term solvency and offset budgetary contributions. This paper uses a simulation method to examine the long-term effect of a low-return environment on the unfunded liabilities and contribution costs of US public pension systems while considering the moderating effects of asset allocation strategies, amortization approaches, and contribution policies.

In the middle of the 20th century, increasing inbreeding rates were identified as a threat to livestock breeding. Consequences include reduced fertility, fitness and phenotypic expression of lethal alleles. An important step in mitigating this inbreeding was the introduction of optimum contribution selection (OCS). OCS facilitates the simultaneous management of genetic gain and inbreeding rates. However, using a standard OCS methodology for regional breeds with historical introgression for upgrading reasons could lead to reinforced selection on introgressed genetic material since those alleles improve the rate of genetic gain and reduce the average kinship in the population. Consequently, regional breeds may become genetically extinct if a standard OCS approach is used. Thus, the advanced OCS (aOCS) approach takes introgressed genetic material into account. The major goals of this study were to (i) gather key information on the feasibility of aOCS under practical conditions of the actual breeding scheme of Vorderwald cattle, (ii) identify superior strategies for implementing the actual scheme and (iii) examine whether historical breeding decisions to increase genetic gain by introgression from commercial breeds could have been avoided by using aOCS. Stochastic simulations were designed in this study to create populations from the historical gene pool by using aOCS. Simultaneously, all practical constraints of a breeding scheme were met. Thus, the simulated populations were comparable with real data. The annual genetic gain was higher in reality (1.56) than in the simulation scenarios (1.12–1.40). The introgressed genetic material increased to 61.3% in reality but was conserved at a final value of 15.3% (±0.78) across simulations. The classical rate of inbreeding and rate of native inbreeding were constrained to 0.092% on an annual basis. This value is equal to an effective population size of 100. The observed values for rates of inbreeding were 0.082–0.087% and 0.087–0.088% for classical and native kinship, respectively. The corresponding figures in reality were 0.067% and 0.184%, respectively. This study suggests that aOCS is feasible for Vorderwald cattle. Strategies for implementation are identified. Finally, we conclude that historical breeding decisions could have been avoided by using aOCS. The genetic gain would have been reduced by at least 12.2%, but the introgressed genetic material, genetic diversity and native genetic diversity would have been more desirable for a breed under conservation.

The importance of timeliness is investigated in the selection of machinery complements for double-crop wheat and soybean production in the southeastern coastal plain. An intertemporal stochastic simulation model was developed to generate probability distributions that were evaluated with stochastic dominance analysis. This research investigated the importance of intertemporal production linkages and inadequate soil moisture on machinery selection. Failure to include these dimensions can result in erroneous machinery choices.

Using a stochastic version of the POLYSYS modeling framework, an examination of projected variability in agricultural prices, supply, demand, stocks, and incomes is conducted for corn, wheat, soybeans, and cotton during the 1998–2006 period. Increased planting flexibility introduced in the 1996 farm bill results in projections of significantly higher planted acreage variability compared to recent historical levels. Variability of ending stocks and stock-to-use ratios is projected to be higher for corn and soybeans and lower for wheat and cotton compared to the 1986–96 period. Significantly higher variability is projected for corn prices, with wheat and soybean prices also being more variable. No significant change in cotton price variability is projected.

Stochastic simulation was used to analyze revenues and costs for a small-scale catfish processing plant under various combinations of operating capacity utilization and price paid for live fish. The probability for a positive level of daily net income ranged from 11 to 100 percent depending on the price paid for live fish and level of operating capacity utilized. Daily average total cost per pound of live fish processed changed by 2.10 percent given a 10 percent change in live fish processed. Short-term cyclical patterns in revenues and costs suggest a need for financial planning to provide for possible year-end revenue shortfalls.

The implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or “Greeks”). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a “bump and revalue” method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.

The trustees and sponsors of defined benefit schemes rely on the advice of the Scheme Actuary to make important decisions concerning the funding of the scheme, the investment of its assets, and the use of surplus assets to improve benefits. These decisions have to be made in the face of considerable uncertainty about financial and demographic factors that will affect the future experience of the scheme and its success in meeting various objectives.

The traditional actuarial valuation combined with actuarial judgement has played an important role in guiding decision making; but we argue that stochastic methods can add value in certain crucial areas, in particular the financial risk management of defined benefit schemes. Rather than dealing with risk by incorporating margins in the valuation basis, a stochastic approach allows the actuary to evaluate specific and quantifiable risk and performance measures for alternative funding and investment strategies.

This paper recommends a framework that, when combined with a suitable stochastic model, measures the risks inherent in contribution rate and asset allocation decisions, allowing better decisions to be made. In doing this, we suggest and apply various risk and performance measures that may be thought appropriate, although our intention is to illustrate their use rather than prescribe them as objective standards. The framework provides the means to explore the trade-offs involved in possible contribution and asset allocation decisions, and points to decision strategies expected to give improved outcomes for the same level of risk. A feature of the approach that marks it out from current asset/liability techniques is that it examines the funding and investment decisions together. It does not derive a contribution rate in the traditional way, but leaves this as free variable, in the same way that the investment decision is taken to be a free variable. Another distinctive feature of our framework is that it is based on projection rather than on valuation, involving stochastic simulation of the experience of the scheme over a time horizon reflecting the concerns of the trustees and the sponsoring employer.

The paper provides a case study (based on a model final salary pension scheme) showing the advantages of the framework, and goes on to explain how the results may practically be communicated to trustees and scheme sponsors.

In this paper a stochastic model office offering UK-style life insurance contracts is used to demonstrate the effect on relative solvency of different investment and bonus strategies. Relative solvency is defined loosely as the probability that an individual insurer does not fall significantly out of line with the rest of the life insurance market, in terms of, for example, asset liability ratios, or payouts to with-profit policyholders. The model uses the Wilkie investment model, extended to incorporate variation between companies in equity performance.

To gain insight into the use of Dynamic Solvency Testing (DST) and Financial Condition Reporting (FCR), a questionnaire was distributed to Appointed Actuaries in United Kingdom life offices. The response rate of the main survey was 76%. An independent-samples t-test for non-respondent bias was conducted and the results suggest that the respondent sample is representative of the survey population. Results from the 62 firms responding revealed: (1) Scenario testing was the most commonly used DST techniques. (2) Most life offices regularly run less than ten scenarios in scenario testing. (3) Most life offices reported using a five-year forecast period in DST. (4) The two most commonly seen difficulties are: difficulties in communicating complex issues to non-specialists, and how to present extremely adverse scenarios without causing undue concern. (5) Nearly all life offices use FCR. (6) Guidance Note 2 is generally considered acceptable. (7) Compared with the results reported by previous studies, the use of DST techniques is now more common in life offices. (8) There is a significant difference in DST/FCR practices between with-profits and non-profit offices.

Alternative Norwegian sheep breeding schemes were evaluated by stochastic simulation of a breeding population with about 120 000 ewes, considering the gain for an aggregate genotype including nine traits and also the rate of inbreeding. The schemes were: a scheme where both young unproven rams (test rams) and proven rams (elite rams) are used in artificial insemination (AI scheme), a scheme with test rams in natural mating in ram circles and elite rams (from one and a half years of age) in AI across all flocks in the country (NMAI2 scheme), a scheme where, in addition to testing rams, the youngest elite rams (one and a half years of age) are also used in natural mating in ram circles, while older elite rams are used in AI (NMAI1 scheme), and a scheme, acting as a control, where both test and elite rams are used in natural mating (NM scheme). Within the NMAI- and AI-schemes, experimentation was performed for percent ewes inseminated to elite rams v. test rams (EM%), numbers of ewes inseminated per elite ram (EAIn), and numbers of ewes mated per test ram by natural service (TNMn) or by AI (TAIn), respectively. With a restriction on the rate of inbreeding (⩽0.8% per generation), the AI scheme gave similar gain to the NMAI2 scheme (and about 40% more than did the NM scheme). Less gain was generated by the NMAI1 scheme, but it was still considerably more than for the NM scheme (about 25%). In the AI scheme, relatively few ewes (200/300) should be inseminated to each test/elite ram, and a low EM% should be chosen (10%). In the NMAI schemes, TNMn should be relatively high (40 to 50), combined with average and somewhat larger than average EAIn (NMAI2: 700 ewes, NMAI1: 900 ewes), and EM% medium (30%).

GAMEFISTO simulation model is presented as a tool to improve the small scale fisheries bioeconomic simulation techniques. The main novelty of the current model is the implementation of game theoretic techniques for forecasting the fishing effort trends and consequently, the fish population levels and the economic outcome, including landings, income and net profits. The model assigns individual fishing strategies to individual vessels according to their technical characteristics. The fishermen within a fishing fleet exploiting a single stock are assumed to be the decision agents, who share not only a fish population (modelled through stock externality) but also a market, through an offer-demand function (market externality). Mediterranean fisheries need to be analysed at vessel level due to the heterogeneity of its fishing fleets. A ten year simulation on red shrimp, Aristeus antennatus, is presented as an application of the presented GAMEFISTO model.

In a stochastic simulation study the effect of simultaneously changing the model for prediction of breeding values and changing the breeding goal was studied. A population of 100 000 cows with registrations on seven traits was simulated in two steps. In the first step of 15 years the population was selected for production and mastitis occurrence using a univariate model for prediction of breeding values for production and a trivariate model using information on mastitis treatments, udder depth and somatic cell score for prediction of breeding values for mastitis occurrence. In the second step six different scenarios were set up and simulated for 15 years combining two different breeding goals and three different models for prediction of breeding values in 20 replicates. Breeding goal 1 had relative economic value per genetic standard deviation on production (19.4) and mastitis occurrence ( − 50) whereas breeding goal 2 had a economic value on production (19.4), udder depth (4.2), mastitis occurrence ( − 50), non return rate (13.0) and days open ( − 16.75). Model 1 was a model similar to the one used in the first 15 years. Model 2 was an approximate multitrait model where solutions for fixed effects from a model corresponding to model 1 were subtracted from the phenotypes and a multitrait model with an overall mean, a year effect, an additive genetic and a residual effect were applied. Model 3 was a full multitrait model. Average genetic trends for total merit and each individual trait over 20 replicates were compared for each scenario. With the number of replicates the genetic responses using model 2 and 3 were not significant different. With a broad breeding goal using, model 2 or model 3 gave a significantly higher response in total merit than using model 1. Using a narrow breeding goal there was no significant difference between models used for prediction of breeding values. Results showed that with a breeding goal with a lot of emphasis on low heritable traits with a high economic value using a multitrait methodology for prediction of breeding values will redistribute the genetic progress in the total merit index. More gain will come from the low heritable traits in the breeding goal and less from traits with higher heritability. With a broad breeding goal and exploiting the available information in the data the inbreeding coefficient increased though not significantly.

Recently, we introduced a phototransduction model that was able to account for the reproducibility of vertebrate rod single-photon responses (SPRs) (Hamer et al., 2003). The model was able to reproduce SPR statistics by means of stochastic activation and inactivation of rhodopsin (R*), transducin (Gα), and phosphodiesterase (PDE). The features needed to capture the SPR statistics were (1) multiple steps of R* inactivation by means of multiple phosphorylations (followed by arrestin capping) and (2) phosphorylation dependence of the affinity between R* and the three molecules competing to bind with R* (Gα, arrestin, and rhodopsin kinase). The model was also able to account for several other rod response features in the dim-flash regime, including SPRs obtained from rods in which various elements of the cascade have been genetically disabled or disrupted. However, the model was not tested under high light-level conditions. We sought to evaluate the extent to which the multiple phosphorylation model could simultaneously account for single-photon response behavior, as well as responses to high light levels causing complete response saturation and/or significant light adaptation (LA). To date no single model, with one set of parameters, has been able to do this. Dim-flash responses and statistics were simulated using a hybrid stochastic/deterministic model and Monte-Carlo methods as in Hamer et al. (2003). A dark-adapted flash series, and stimulus paradigms from the literature eliciting various degrees of light adaptation (LA), were simulated using a full differential equation version of the model that included the addition of Ca2+-feedback onto rhodopsin kinase via recoverin. With this model, using a single set of parameters, we attempted to account for (1) SPR waveforms and statistics (as in Hamer et al., 2003); (2) a full dark-adapted flash-response series, from dim flash to saturating, bright flash levels, from a toad rod; (3) steady-state LA responses, including LA circulating current (as in Koutalos et al., 1995) and LA flash sensitivity measured in rods from four species; (4) step responses from newt rods (Forti et al., 1989) over a large dynamic range; (5) dynamic LA responses, such as the step-flash paradigm of Fain et al. (1989), and the two-flash paradigm of Murnick and Lamb (1996); and (6) the salient response features from four knockout rod preparations. The model was able to meet this stringent test, accounting for almost all the salient qualitative, and many quantitative features, of the responses across this broad array of stimulus conditions, including SPR reproducibility. The model promises to be useful in testing hypotheses regarding both normal and abnormal photoreceptor function, and is a good starting point for development of a full-range model of cone phototransduction. Informative limitations of the model are also discussed.

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

In the last few years we have witnessed growing interest in Dynamic Financial Analysis (DFA) in the nonlife insurance industry. DFA combines many economic and mathematical concepts and methods. It is almost impossible to identify and describe a unique DFA methodology. There are some DFA software products for nonlife companies available in the market, each of them relying on its own approach to DFA. Our goal is to give an introduction into this field by presenting a model framework comprising those components many DFA models have in common. By explicit reference to mathematical language we introduce an up-and-running model that can easily be implemented and adjusted to individual needs. An application of this model is presented as well.