Search

In quantitative finance practice, model calibration is a key challenge. This is especially so when a local regime-switching model needs to be calibrated because designing an efficient and reliable algorithm to obtain local volatility values as a function of underlying price and time is important for the model to be successfully used in practice. Therefore, this paper proposes a new algorithm for calibrating local regime-switching models with observed option prices available for a particular market that is suitable for this type of model. The newly proposed algorithm is tested with calibrations performed on synthetic as well as real market data. Our empirical test results indicate that the algorithm has great potential to be used in financial risk management. [ABSTRACT FROM AUTHOR]

This paper presents a semi-parametric method for bootstrapping non-stochastic estimates of Malmquist indices and the second-stage regressions with a coherent data-generating process (DGP) for panel data. It emphasizes the importance of using censoring techniques instead of truncation in the DGP. To keep the panel structure, the fixed effects censored least square (CLS) method is preferred in the algorithm. Two smoothing processes in the DGP using fixed effects CLSs and cross-sectional censored least absolute deviations are proposed and compared. This semi-parametric bootstrap process can be used to delete artificial correlation amongst the estimated efficiencies in panel data. Although the exposition gives only output-oriented indices, the method can easily be extended to the input-oriented model. Finally, an empirical case study is carried out on Irish dairy farms. [ABSTRACT FROM AUTHOR]

Hazardous material (hazmat) transportation has received several attention in the past. On the one hand, this is motivated by the practical interest that hazmat transportation covers for safety reasons; on the other hand, it has attracted the study of those researchers working on vehicle routing since relevant hazmat transportation issues are concerned with finding routes with minimum cost and minimum risk. The former objective is mainly related to the carrier point of view, whereas the latter objective takes into account the government point of view. In this paper, we propose a new approach for planning routes for hazmat shipments that selects k efficient paths with respect to the minimization of length, time (cost) and risk; in particular, the selection is made by choosing k representative paths among the set of efficient paths, with high spatial dissimilarity. This allows one to guarantee an equitable distribution of the risk over the network. The proposed approach first exploits the Martins’ algorithm to find the set of efficient paths, and the k-means algorithm to partition the latter set into k classes of paths, minimizing the total variance of the objective vector values of the paths in the same class. Next, one path from each one of the k classes is chosen by heuristically solving the problem of selecting paths maximizing the total spatial dissimilarity. Computational results are presented on random graphs and on a real-life case study. [ABSTRACT FROM PUBLISHER]

This paper proposes two extensions to the SMPS format for stochastic programs to permit modelling of autoregressive-moving average (ARMA) processes. Sampling-based algorithms can thus proceed independently of any underlying modelling system, increasing efficiency. An illustrative example demonstrates the power of the new constructs. [ABSTRACT FROM AUTHOR]

Variable neighbourhood search (VNS) is one of the most recent metaheuristics used for solving combinatorial optimization problems in which a systematic change of neighbourhood with a local search is carried out. However, as happens with other metaheuristics, it takes a long time to reach some useful solutions while solving some sort of hard combinatorial problems such as job shop scheduling (JSS). Parallelization is one of the most considerable policies to overcome this matter. In this paper, firstly, a number of VNS algorithms are examined for JSS problems and then four different parallelization policies are taken into account to determine efficient parallelization for VNS algorithms. The experimentation reveals the performance of various VNS algorithms and the efficiency of policies to follow in parallelization. In the end, the unilateral-ring topology, a noncentral parallelization method, is found as the most efficient policy. [ABSTRACT FROM AUTHOR]

Variable neighbourhood search (VNS) is a modern metaheuristic based on systematic changes of the neighbourhood structure within a search to solve optimization problems. The aim of this paper is to propose and analyse a VNS algorithm to solve scheduling problems with parallel machines and sequence- dependent setup times, which are of great importance on the industrial context. Three versions of a greedy randomized adaptive search procedure algorithm are used to compare with the proposed VNS algorithm to highlight its advantages in terms of generality, quality and speed for large instances. [ABSTRACT FROM AUTHOR]

We develop a mathematical model to study optimal preventive maintenance (PM) strategy under a two-dimensional stair-case warranty policy considering both age and usage of a product. During the warranty term, sellers implement preventive maintenance within the stair-case region of the warranty policy and upon failure a product is repaired minimally and immediately. Our objective is to find the optimal PM strategy that minimizes the seller's cost of warranty while jointly considering the age and usage intervals of the PM policy and the level of PM executed. We also discuss how our results compare to those in a two-dimensional warranty policy with a rectangular region, and we find that the stair-case policy is preferable for sellers. An algorithm is provided to find the optimal solution and a numerical example is presented to illustrate how to find an optimal strategy with our proposed method. We show numerically that the expected total warranty cost is convex both in the age and the usage of the product under certain conditions. [ABSTRACT FROM AUTHOR]

The aim of this paper was to propose a condition-based maintenance policy for a gradually deteriorating system subject to change in the deterioration rate using on-line detection algorithms. The parameters of the deterioration rate after the change is unknown. The main purpose is to estimate these unknown parameters in order to adapt the condition-based maintenance policy and above all to optimize a global cost criterion. [ABSTRACT FROM PUBLISHER]

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Up till now, neighbourhood search has been the most efficient optimization framework for solving the problem. The discovery and innovative application of neighbourhood properties is a key issue in the design of such algorithms. Effective neighbourhood properties help one to exclude unpromising solutions in the neighbourhood, and thus accelerate the convergence of the whole searching process. In this paper, we aim at solving the JSSP with the objective of minimizing total weighted tardiness, which includes most other regular objective functions as special cases. A neighbourhood property of the problem is discovered based on the duality of linear programming models. Then, the neighbourhood property is utilized by a tree search procedure, which is finally embedded into the particle swarm optimization framework. According to extensive computational experiments and the real-world application to a large-scale manufacturing firm in China, the proposed approach is effective for solving the JSSP. [ABSTRACT FROM PUBLISHER]

Coxian phase-type distributions are becoming a popular means of representing survival times within a health care environment. They are favoured as they show a distribution as a system of phases and can allow for an easy visual representation of the rateof flow of patients through a system. Difficulties arise, however, in determining the parameter estimates of the Coxian phase-type distribution. This paper examines ways of making the fitting of the Coxian phase-type distribution less cumbersome byoutlining different software packages and algorithms available to perform the fit and assessing their capabilities through a number of performance measures. The performance measures rate each of the methods and help in identifying the more efficient. Conclusions drawn from these performance measures suggest SAS to be the most robust package. It has a high rate of convergence in each of the four example model fits considered, short computational times, detailed output, convergence criteria options, along with a succinct ability to switch between different algorithms. [ABSTRACT FROM PUBLISHER]

This paper deals with analysis and control of an MX/G/1 retrial queue with vacations where batches of customers arrive according to a compound Poisson process. Retrial times are governed by an arbitrary probability law which is independent of the number of customers in the retrial group. We consider an energetic interpretation in the sense that the service of a customer requires not only a random time but also a random amount of work (or energy) with an arbitrary probability distribution. The server is turned off and takes a vacation when the system becomes empty. The random work required for each vacation is also arbitrarily distributed. We show that the evolution of the queue can be described at some regenerative points by a stochastically recursive relation. This gives a discrete event simulation algorithm for our queue for which we derive an ergodicity condition. We obtain an explicit formula for the generating function of the number of customers in orbit in steady state and demonstrate a stochastic decomposition property. Finally, we obtain performance measures and consider optimal control of vacation and retrial policies. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for the allocation of sales representatives is presented. The model takes into account some special features of pharmaceutical marketing, such as customer profiling (physicians), sales response functions and multi-product (drug) promotion procedures. The main peculiarity of the model is that it is suitable to those markets (such as European markets) where the detailed information about historical physician prescriptions is not available to pharmaceutical companies. A heuristic procedure has been designed and run to plan nationwide representative calls to more than 46000 physicians. A computational study, based on real data from a major pharmaceutical company, shows the feasibility of this algorithmic approach, resulting in significantly enhanced productivity. Moreover, the algorithm can be also employed as a tool to evaluate costly strategic options concerning sales force sizing and training. [ABSTRACT FROM PUBLISHER]

Over the past decade, several stochastic approaches have been proposed for two-stage stochastic programs. Many of these algorithms have attractive computational as well as conceptual properties (e.g. convergence with probability one). This paper expands the realm of such approaches to multistage convex stochastic programming problems. We present a stochastic scenario decomposition (SSD) algorithm which is a statistically motivated cutting plane algorithm for the solution of multistage stochastic programs. The method is based on solving a dual problem in which the variables correspond to multipliers associated with the non-anticipativity constraints of the primal problem. Our analytical results verify conditions under which SSD identifies an optimal solution asymptotically. We also overcome some computational hurdles resulting from increases in the column dimension of the SSD master problem. We propose a variable aggregation scheme that allows us to solve much smaller master programs without sacrificing solution quality. Our computational results demonstrate the effectiveness of this aggregation scheme in solving the SSD master program. [ABSTRACT FROM PUBLISHER]

A class of semiparametric fractional autoregressive models with generalized autoregressive conditional heteroskedastic (GARCH) errors, which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence and heteroskedastic model errors, is very powerful for modelling financial time series. This paper discusses the model fitting, including an efficient algorithm and parameter estimation of GARCH error term, so that the model can be applied in practice. We then illustrate the model and estimation methods with a few of different finance data sets. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of variable selection and the determination of the coefficients for these variables that provide the best linear discrimination function with the objective of obtaining a high classification success rate. Given the relation that exists between both problems, they will be performed simultaneously. In order to resolve them, two algorithms based on the metaheuristic approaches variable neighbourhood search and tabu search have been designed. These methods have proved to obtain significantly better results than two of the most classic methods for obtaining discriminant linear functions: classic discriminant analysis and logistic regression. [ABSTRACT FROM AUTHOR]

Mixed integer programming (MIP) models are extensively used to aid strategic and tactical decision making in many business sectors. Solving MIP models is a computationally intensive process and there is a need to develop solution approaches that enable larger models to be solved within acceptable timeframes. In this paper, we describe the implementation of a two-stage parallel branch and bound (PB&B) algorithm for MIP. In stage 1 of the algorithm, a multiple heuristic search is implemented in which a number of alternative search trees are investigated using a forest search in the hope of finding a good solution quickly. In stage 2, the search is reorganized so that the branches of a chosen tree are investigated in parallel. A new heuristic is introduced, based on a best projection criterion, which evaluates alternative B&B trees in order to choose one for investigation in stage 2 of the algorithm. The heuristic also serves as a way of implementing a quality load balancing scheme for stage 2 of the algorithm. The results of experimental investigations are reported for a range of models taken from the MIPLIB library of benchmark problems. [ABSTRACT FROM AUTHOR]

In 1956, Kelly developed a staking system to calculate the optimal fraction of wealth to bet on each of a series of favourable bets. In line with historical betting markets, Kelly considered only back bets on events with a single favourable outcome. The recent advent of betting exchanges makes a much wider range of bets available. We extend Kelly's algorithm to betting on a single market, with both back and lay bets available, and we demonstrate the superiority of doing so with betting data collected during the 2009/2010 English Premiership season. We further show that a more general problem with multiple dependent markets can be described as linearly constrained convex optimization. As numerical solutions to these problems are nearly as advanced as those for linear systems, we argue that it is possible to consider this more general case to be solved (at least numerically). We demonstrate how it is possible to formulate such a problem in the case of football bets and we demonstrate the superior growth rate of such a strategy. Two further issues which Kelly did not have to consider are commission and the variability of market size. We modify the objective function which we have been maximizing to take account of commission and further improve the growth rate of wealth in our test data. We begin a discussion on market size, adding constraints to take account of it in our numerical solution and observe the effect. We note the level of wealth at which further growth is impeded by the market size. [ABSTRACT FROM AUTHOR]

We investigate the state-of-the-art in score-based soccer match outcome modelling to identify the top-performing methods across diverse classes of existing approaches to the problem. Namely, we bring together various statistical methods based on Poisson and Weibull distributions and several general ranking algorithms (Elo, Steph ratings, Gaussian-OD ratings) as well as domain-specific rating systems (Berrar ratings, pi-ratings). We review, reimplement and experimentally compare these diverse competitors altogether on the largest database of soccer results available to identify true leaders. Our results reveal that the individual predictions, as well as the overall performances, are very similar across the top models tested, likely suggesting the limits of this generic approach to score-based match outcome modelling. No study of a similar scale has previously been done. [ABSTRACT FROM AUTHOR]

A shootout is a popular mechanism to identify a winner of a match between two teams. It consists of rounds in which each team gets, sequentially, an opportunity to score a point. It has been shown empirically that shooting first or shooting second in a round has an impact on the scoring probability. This raises a fairness question: is it possible to specify a sequence such that identical teams have equal chance of winning? We show that, for a sudden death, no repetitive sequence can be fair. In addition, we show that the so-called Prohuet–Thue–Morse sequence is not fair. There is, however, an algorithm that outputs a fair sequence whenever one exists. We also analyze the popular best-of- |$k$| shootouts and show that no fair sequence exists in this situation. In addition, we find explicit expressions for the degree of unfairness in a best-of- |$k$| shootout; this allows sports administrators to asses the effect of the length of the shootout on the degree of unfairness. [ABSTRACT FROM AUTHOR]

Optimal asset replacement is analysed under non-exponential technological improvement, whereby the asset capital cost and the operational cost reduce for newer assets, and the relative rate of this decrease varies with time. We establish that the optimal lifetime of sequentially replaced assets increases if the relative rate of technological change decreases, and converse. Next, the two-cycle replacement algorithm is employed to take the unequal asset lifetime into account. The algorithm is adjusted to the case of several discrete estimates of changing asset costs and demonstrates good performance in various scenarios of improving technology. [ABSTRACT FROM AUTHOR]

An improved Weiszfeld algorithm, termed the fortified Weiszfeld algorithm, for the solution of the single facility Weber problem with Euclidean distances is proposed. The new approach is based on a parabolic approximation of the objective function and testing demand points for optimality. Computational experiments show the superiority of the fortified approach to the original Weiszfeld algorithm. [ABSTRACT FROM AUTHOR]

Class handicapping methods enable different classes of athletes to compete on equal terms. Different sports use a variety of algorithms, which are usually based on historical data and subjective opinions. A recent proposal is to use an interactive shrinkage method for class handicapping, as this is generic across sports and uses data from the current competition only. This article presents a mathematical justification of the interactive shrinkage method for class handicapping, based on an objective Bayesian analysis of a suitable probability model. It also investigates how this approach performs in the context of paralympic sports, by analyzing actual competition data and comparing the results with those from existing schemes. Our findings suggest that this method is robust, convenient and fair. We provide a discussion in this article to explore possible extensions of this procedure. [ABSTRACT FROM AUTHOR]

The purpose of this article is to determine optimal maintenance policies for deteriorating systems subject to failure. Complex systems that deteriorate with usage and age are often subject to random failures of several kinds. Since it is costly to repair or replace failed systems, preventive maintenance is usually carried out while the systems are still operational. This article will be useful in providing maintenance engineers with a methodology to model failing systems and efficiently determine optimal maintenance policies. The problem is formulated and solved in a semi-Markov decision framework with the optimality criterion being the minimization of the long-run expected average cost per unit time. The model developed in this article, which is an extension of recent maintenance models, can be applied to systems that have any finite number of major and/or minor failure states and to systems that permit general repair in operational and major failure states. A new computational approach using an embedded technique is developed that is computationally preferable to the standard policy iteration algorithm when determining the optimal maintenance policy for systems with many states. [ABSTRACT FROM AUTHOR]

An algebraic modelling language (AML) is a domain-specific computer programming language for describing and solving mathematical programming models. We propose extending AMLs so that solution algorithms that are based on iteratively manipulating, modifying and solving a model are supported at a high abstraction level. We specifically focus on stochastic programming models with random parameters formulated as discrete scenarios and mathematical decomposition algorithms, which are commonly applied to solve such models. We identify the necessary language constructs and develop a design based on the open-source modelling software APLEpy. The proposed design, although specifically addressing decomposition algorithms, proves useful for implementing heuristic solution algorithms as well. The object-oriented nature of the design enables the algorithms that are coded with the proposed extensions to work with any other model that satisfies the assumptions of the initial model. This flexible and robust design helps inexperienced modellers to easily apply an advanced solution algorithm, and experienced modellers to build sophisticated algorithms quickly within the same development environment that is used to describe the model under consideration. [ABSTRACT FROM AUTHOR]

Derivative pricing models require calibration to market conditions in order to determine quantities such as hedging positions and the prices of other instruments. For stochastic models and/or complex derivatives whose prices are not of an analytic form, prices must be computed via simulation and the calibration is more difficult. A method to facilitate the calibration of simulation-based pricing models is proposed. The algorithm uses a statistically designed experiment to select the points at which simulations are performed. The method is quite general as it is independent of the stochastic model for the underlying and allows for different objective functions that can incorporate information such as open interest and volume. Furthermore, market prices from European- and/or American-style derivatives covering a range of strike prices and maturities can be handled by this technique. Examples show the procedure is successful at calibrating well-known asset pricing models to both simulated and market data. [ABSTRACT FROM AUTHOR]

A variable neighbourhood search (VNS) algorithm has been developed to solve the redundancy allocation problem (RAP). The VNS method is perfectly suited to those combinatorial problems with potential neighbourhood structures, as in the case of the RAP. The most studied configuration of the RAP is a series system of s-independent k-out-of-n:G subsystems the so-called series-parallel system. The RAP is to select the optimal combination and redundancy levels of components to meet system-level constraints. Two types of objectives are considered in this study—system reliability maximization and system cost minimization. The VNS algorithm is tested on sets of benchmark problems and compared to the best heuristics in the literature such as tabu search, multiple weighted objective heuristic, ant colony optimization and genetic algorithm. Computational results show the advantages and benefits of VNS for solving both types of RAP while considering both solution quality and computational efficiency. [ABSTRACT FROM AUTHOR]

We consider the problem of separating two sets of points in a Euclidean space with a hyperplane that minimizes the sum of p-norm distances to the plane of points lying on the 'wrong' side of the plane. A variable neighbourhood search heuristic is used to determine the plane coefficients. For a set of examples with L1-norm, L2-norm and L∞-norm, for which the exact solution can be computed, we show that our algorithm finds it in most cases and gets good approximations in the others. The use of our heuristic solutions for problems in these norms can dramatically accelerate exact algorithms. Our method can be applied on very large instances that are intractable by exact algorithms. Since the proposed approach works for truly arbitrary norms (other than the traditional 1, 2 and ∞), we can explore for the first time the effects of the choice of p on the generalization properties of p-norm hyperplane separation. [ABSTRACT FROM AUTHOR]

The location of a facility in the plane when service availability is a convex decreasing function of the distance (distance decay) is considered. The total cost of the system consists of three components: (i) the cost of waiting in line for service, (ii) the cost of providing the service and (iii) the cost of lost demand. A generalized Weiszfeld algorithm and a global optimization technique are constructed and tested on problems of up to 10000 demand points assuming exponential decay in service. Both algorithms are very efficient. [ABSTRACT FROM AUTHOR]