A stochastic simulation procedure for pension schemes

This paper deals with the calculation of some quantities concerning pension schemes by means of stochastic simulation. A very simple procedure, suitable for a typical pension scheme model, is here proposed. It supplies us with a noteworthy time-saving calculation tool, as opposed to a simulation procedure based on a different approach. Comparisons between the calculation times required in numerical experiences by these two different procedures, as well as some results thereby obtained, are then presented.     

Using subsystem linear regression metamodels in stochastic simulation

This article explores the use of metamodels as simulation building blocks. The metamodel replaces a part of the simulation model with a mathematical function that mimics the input–output behavior of that part, with respect to some measure of interest to the designer. The integration of metamodels as components of the simulation model simplifies the model and reduces the simulation time. Such use of the metamodels also gives the designer a better understanding of the behavior of those parts of the model, making the simulation model as a whole more intelligible. The metamodel-based simulation model building process is examined, step by step, and the designer options are explored. This process includes the identification of the metamodel candidates and the construction of the metamodels themselves. The assessment of the proposed approach includes the evaluation of the integration effort of the metamodel into the metamodel-based simulation model, and the accuracy of the output data when compared to the original system.     

Using DEA to assess NATO burden-sharing

As the member making many of the most visible contributions to NATO, the USA has often claimed that they shoulder the heaviest ‘burden’ in maintaining the objectives of the alliance. This claim has been backed by research which has concentrated on contributions such as defence expenditure and benefits such as protection from external threats. However, modern alliances entail the exchange of multiple forms of alliance benefits and liabilities and therefore the study of ‘burden-sharing’ in these alliances is a more complicated accounting problem than has been acknowledged by previous research. In this paper, burden-sharing is studied using Data Envelopment Analysis (DEA). This is a novel application of DEA. Instead of calculating relative ‘efficiencies’, the analysis produces a ‘net-burden index’ for each member nation of NATO. The results of the analysis indicate that whilst the USA shoulders a heavy burden, some other member nations, including Canada and Spain, may in fact shoulder a heavier burden.     

Using degradation models to assess pipeline life

Longitudinal inspections of thickness at particular locations along a pipeline provide useful information to assess the remaining life of the pipeline. In applications with different mechanisms of corrosion processes, we have observed various types of general degradation paths. We present two applications of fitting a degradation model to describe the corrosion initiation and growth behavior in a pipeline. We use a Bayesian approach for parameter estimation for the degradation model. The failure‐time and remaining lifetime distributions are derived from the degradation model, and we compute Bayesian estimates and credible intervals of the failure‐time and remaining lifetime distributions for both individual segments and for the entire pipeline circuit.     

Error and convergence of two numerical schemes for stochastic differential equations

We examine the convergence and error rate of two stochastic numerical schemes using the method of proof used by G. N. Mil'shtein 1 . © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006.     

Using linear programming to analyze and optimize stochastic flow lines

This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time, to determine a production rate estimate. As our methodology is purely numerical, it offers the full modeling flexibility of stochastic simulation with respect to the probability distribution of processing times. However, unlike discrete-event simulation models, it also offers the optimization power of linear programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines.     

Discretization and simulation of stochastic differential equations

We discuss both pathwise and mean-square convergence of several approximation schemes to stochastic differential equations. We then estimate the corresponding speeds of convergence, the error being either the mean square error or the error induced by the approximation on the value of the expectation of a functional of the solution. We finally give and comment on a few comparative simulation results.     

Two-stage stochastic equilibrium problems with equilibrium constraints: modeling and numerical schemes

This article presents a two-stage stochastic equilibrium problem with equilibrium constraints (SEPEC) model. Some source problems which motivate the model are discussed. Monte Carlo sampling method is applied to solve the SEPEC. Convergence analysis on the statistical estimators of Nash equilibria and Nash stationary points are presented.     

Euler schemes and large deviations for stochastic Volterra equations with singular kernels

In this paper, an Euler type approximation is constructed for stochastic Volterra equation with singular kernels, which provides an algorithm for numerical calculation. Then, the large deviation estimates of small perturbation to equations of this type are obtained. We finally apply them to SDEs with the kernel of fractional Brownian motion with Hurst parameter H∈(0,1).     

Using spatial games to model dynamic evolutionary systems

Modelling the dynamics of evolutionary competing species on a physical grid is a challenging modelling problem. This paper presents a novel modelling approach for synthesizing evolutionary dynamics of competing species using a spatial game perspective. This modelling approach describes the movement of players (‘species’ in our context) across a lattice. The model is based on a payoff function which controls the move likelihood and direction of the players (‘predators’ and ‘preys’). Using simulated results, the paper provides a comparison between the spatial game model and an existing predator-prey dynamic model. Finally, a case study is performed to illustrate the application of this formalism and validate the model.     

Numerical simulation of stochastic evolution equations associated to quantum Markov semigroups

We address the problem of approximating numerically the solutions of stochastic evolution equations on Hilbert spaces , with respect to Brownian motions, arising in the unraveling of backward quantum master equations. In particular, we study the computation of mean values of , where is a linear operator. First, we introduce estimates on the behavior of . Then we characterize the error induced by the substitution of with the solution of a convenient stochastic ordinary differential equation. It allows us to establish the rate of convergence of to , where denotes the explicit Euler method. Finally, we consider an extrapolation method based on the Euler scheme. An application to the quantum harmonic oscillator system is included.

     

Using tabu search to schedule activities of stochastic resource-constrained projects

In this paper, a higher level heuristic procedure “tabu search” is proposed to provide good solutions to resource-constrained, randomized activity duration project scheduling problems. Our adaptation of tabu search uses multiple tabu lists, randomized short-term memory, and multiple starting schedules as a means of search diversification. The proposed method proves to be an efficient way to find good solutions to both deterministic and stochastic problems. For the deterministic problems, most of the optimal schedules of the test projects investigated are found. Computational results are presented which establish the superiority of tabu search over the existing heuristic algorithms.     

Risk measurement and management of defined benefit pension schemes: a stochastic approach

The traditional actuarial valuation for defined benefit pensionschemes operates on the basis of a set of deterministic calculationscombined with actuarial judgment. It has played an importantrole in guiding decision-making as far as the level of fundingis concerned. The paper argues that stochastic methods can addvalue in certain crucial areas, in particular the financialrisk management of such schemes. The traditional approach torisk is to incorporate margins in the valuation assumptions;however, a stochastic approach allows the user to evaluate specificand quantifiable risk and performance measures in respect ofalternative funding and investment strategies. The paper introducesa framework that measures the risks inherent in asset allocationand contribution rate decisions, allowing decisions to be madeon a more informed basis. In doing this, we suggest and applysome potential risk and performance measures. This frameworkprovides the means to explore the trade-offs involved in possiblecontribution and asset allocation decisions and leads to decisionstrategies that are expected to give improved outcomes for thesame level of risk. A realistic case study is used to illustratethe properties of the methodology and how it might be used.     

Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis

We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations (FBSDEs). Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18: 143–177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes.     

Weak local linear discretizations for stochastic differential equations: Convergence and numerical schemes

Weak local linear (WLL) discretizations are playing an increasing role in the construction of effective numerical integrators and inference methods for stochastic differential equations (SDEs) with additive noise. However, due to limitations in the existing numerical implementations of WLL discretizations, the resulting integrators and inference methods have either been restricted to particular classes of autonomous SDEs or showed low computational efficiency. Another limitation is the absence of a systematic theoretical study of the rate of convergence of the WLL discretizations and numerical integratos. This task is the main purpose of the present paper. A second goal is introducing a new WLL scheme that overcomes the numerical limitations mentioned above. Additionally, a comparative analysis between the new WLL scheme and some conventional weak integrators is also presented.     

Survival and coexistence in stochastic spatial Lotka–Volterra models

A spatially explicit, stochastic Lotka–Volterra model was introduced by Neuhauser and Pacala in Neuhauser and Pacala (Ann. Appl. Probab. 9, 1226–1259, 1999). A low density limit theorem for this process was proved by the authors in Cox and Perkins (Ann. Probab. 33, 904–947, 2005), showing that certain generalized rescaled Lotka–Volterra models converge to super-Brownian motion with drift. Here we use this convergence result to extend what is known about the parameter regions for the Lotka–Volterra process where (i) survival of one type holds, and (ii) coexistence holds. Supported in part by an NSERC Research grant.     

Structured construction and simulation of nondeterministic stochastic activity networks

In this work we deal with nondeterministic stochastic activity networks (NDSANs). Their stochastic character results from activity durations, which are given by nonnegative continuous random variables. The nondeterministic behavior of an NDSAN is a consequence of its variable topology, based on two additional features. First, by associating choice probabilities with the immediate successors of an activity, some branches of execution are not always taken. Second, by allowing iterated executions of a group of activities according to predetermined probabilities, the number of times an activity is to be executed is not determined a priori. These properties lead to a wide variety of activity networks, capable of modelling many real situations in process engineering and project management. We describe a simple, recursively structured construction of NDSANs, which both provides a coherent syntactic mechanism to incorporate the two abovementioned nondeterminism features and allows the analytic formulation of completion time. This construction also directly gives rise to a recursive simulation algorithm for NDSANs, whose repeated execution produces an estimate of the probability distribution of the completion time of the network. We also report on real-world case studies, using the Komolgorov–Smirnov statistic for validation.