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With outsourcing of work having become ubiquitous, and more importantly, given its potential to become controversial, the need for such outsourcing decisions to be drafted carefully, managed effectively and controlled accurately cannot be underscored. In this context, this paper has constructed a mathematical model of organizations with 'outsource' employees to study the problem of the monitoring and control of the extent of outsourcing, and the number and distribution of outsource manpower. Control policies for maintaining desired blends of internal and outsource manpower have been mathematically derived, thereby obviating the need for further statistical validation. The cost savings that could be expected to accrue due to outsourcing, as also the problem of optimal outsourcing have been investigated and illustrated with numerical examples. This paper thereby studies a problem of contemporary relevance and importance, and organizations could use the suggested models as a decision-making tool, to generate alternative trade-off scenarios between cost savings due to outsourcing on the one hand, and the need to restrict the extent of outsourcing on the other. [ABSTRACT FROM AUTHOR]

Accepted by: Phil Scarf We model tactical changes in association football as a Markov game. The pitch is discretized into nine zones and the states of the Markov game are defined according to the zone in which the ball is located in-play, the team in possession and the score. We first model tactical changes in a Markov decision process framework, wherein one team maximizes their probability of winning. Then, we model tactical changes in a two-person zero-sum Markov game framework, wherein both teams maximize their probability of winning. Fundamental to our modelling is the notion that tactical changes impact upon transition rates. We verify the models using data from matches in a season of the Japan Professional Football League. We define a change in transition rates that can be realized by changes in tactics, and illustrate an example of optimal tactical changes when both teams can vary their tactics. The models we develop in the paper can support managers who are considering important decisions about substitutions and changes to formation, for example, when a match is in-play. [ABSTRACT FROM AUTHOR]

We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem. [ABSTRACT FROM AUTHOR]

Introduces series of articles published in the July 2005 issue of the "IMA Journal of Management Mathematics." Construction of a two-timescale Markov chain model to capture hospital patient flows; Discussion of the robustness of length of stay as a performance indicator for costing and hospital management; Presentation of a non-linear optimization model for investigating reimbursement systems and the optimal allocation of budgets and in-patients across a region.

In dynamic decision problems, it is challenging to find the right balance between maximizing expected rewards and minimizing risks. In this paper, we consider NP-hard mean-variance (MV) optimization problems in Markov decision processes with a finite time horizon. We present a heuristic approach to solve MV problems, which is based on state-dependent risk aversion and efficient dynamic programming techniques. Our approach can also be applied to mean-semivariance (MSV) problems, which particularly focus on the downside risk. We demonstrate the applicability and the effectiveness of our heuristic for dynamic pricing applications. Using reproducible examples, we show that our approach outperforms existing state-of-the-art benchmark models for MV and MSV problems while also providing competitive runtimes. Further, compared to models based on constant risk levels, we find that state-dependent risk aversion allows to more effectively intervene in case sales processes deviate from their planned paths. Our concepts are domain independent, easy to implement and of low computational complexity. [ABSTRACT FROM AUTHOR]

Given a general cost-reward structure, this paper proposes an integrated maintenance scheduling model for deteriorating multi-state production systems. The paper develops extensions of the existing modelling techniques from non-repairable systems to repairable production systems. The development includes estimation of a value function and so the behaviour prediction of revenue resulting from the system. The estimated value function allows the optimization of system performance by exploiting controllable variables. Two types of repair actions are considered: (i) unplanned minimal repairs and (ii) planned minor and partial repairs at scheduled times to respectively retain the system or restore it to an acceptable level of performance. Planned repair actions incur costs associated with the post-planned repair state and the level of repair. Under minor repair model and two variants of the partial repair models, a system of Laplace transforms of expected net reward (profit), given the initial process state, is established from a system of integral equations. The aforementioned technique recursively provides a solution to the expected net reward. In the two-state model, explicit formulas for expected net reward are given when the initial state is |$X_{0}=1,2$|⁠. With respect to the estimated value function, an optimal solution to the operating time of the system is obtained. Results are developed to give insight into applicability of the devised model to a four-state problem. Sensitivity analysis along with a comparative study of explored repair models are given in support of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, a bivariate semi-Markov reward chain (BVSMC) model is presented. Equations for the higher order moments of the reward process are presented for the first time and applied to the problem of modelling the credit spread evolution of an obligor by considering the dynamic of its own credit rating and that of a dependent obligor called the counterpart. The paper shows how to compute the expected value of the accumulated credit spread (expressed in basis points) that the obligor should expect to pay in addition to the risk free interest rate. Higher order moments of the accumulated credit spread process convey important financial information in terms of variance, skewness and kurtosis of the total basis points the obligor should with pay in a given time horizon. The paper contributes to the literature by extending on previous results on the semi-Markov reward chains, BVSMC and credit spread modelling by providing unifying approach to these problems. The model and the validity of the results are illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

This paper considers a production inventory with positive service time. The time for producing each item is assumed to follow a ‘Markovian production scheme’. Because of this, correlation automatically gets into the production process. The customer arrival process follows a Markovian arrival process. When inventory falls to s, the production process is switched on, and is switched off when the on-hand inventory reaches S. The service time to each customer has a phase-type distribution. We investigate the system stability. Under the condition of stability, we investigate the system state distribution. Next, several performance measures are computed, such as the fraction of time server is on vacation; fraction of time the inventory level is zero; fraction of time the production process is On; expected number of customers in the system while server is on vacation and also while it is busy. Numerical results indicate, among other things, the effect of the control variables s and S on the fraction of time the system goes out of inventory and on expected loss rate of customers. [ABSTRACT FROM AUTHOR]

Recent research by the author was concerned with systems modelled by two processes, the ‘supply’ process and the ‘demand’ process. The systems modelled thereby were such that the goods produced were not storable and were lost if not consumed immediately. In the present paper, we continue this earlier research, now assuming that supply is deterministic and demand is modelled by an irreducible Markov process with a finite, partitioned state space. Combining an earlier result with ‘propositional calculus’, a closed-form expression is obtained for the probability that demand will be met by supply during the first k supply periods. As an application, two repair disciplines for a small computer network will be examined. The computational tool used is SCILAB, a free numerical package run on LINUX. [ABSTRACT FROM PUBLISHER]

This paper reports on a model to assess the current and future states of a monitored system based on measured condition monitoring information to date. The true state of the system is unobservable, but is assumed to be related to the measured condition monitoring information in a stochastic way. We further assume that the transition of the system state follows a time-dependent Markov chain which has only three states, namely good, defective and failed. This assumption effectively defines a two-stage failure process which is widely used in delay time modelling of maintained systems. Three modelling techniques are used to establish the model. First, we use a hidden Markov model to describe the transitions between system states. Second, the transition matrix is established based on the well-known delay time concept. The last one is the use of the filtering technique to construct the relationship between measured condition information and the underlying true state of the system. We also discuss the procedure for model parameter estimation. A numerical example is presented to demonstrate the modelling ideas. [ABSTRACT FROM AUTHOR]

A good estimate of the length of stay (LOS) of elderly people in institutional long-term care (ILTC) is essential to both care providers (care home owners) and purchasers (local authorities in the UK) in order to forecast their resource availability and future requirements. Existing methods usually rely on cohort data, which needs to be collected on a continuous basis for several years and are often not available electronically. In this paper we develop an approach based on multi-census data to fit a Markov model in continuous-time for the LOS of elderly people in ILTC (residential and nursing care), We use 3 year placement data provided by London Borough of Merton Social Services to compare the estimates of the model parameters obtained using multi-census data with those derived from cohort data, hence to validate the multi-census approach in this context. The implications of the proposed multi-census approach and its advantages in the context of long-term care planning are discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a method for identifying the optimal strategy for substituting players in a baseball game, taking into consideration the handedness of players, which is one of the main factors in terms of managerial decision-making for substitution. Using a Markov chain model, we incorporate the effect of the handedness of players by introducing the concept of the defensive earned run average as a measure of the defensive ability of pitchers and calibrating the batting probabilities of players depending on their handedness. We then develop a dynamic programming formulation including the effect of the handedness of players. This method is illustrated using a match based on the real line-ups of the Colorado Rockies and the San Francisco Giants in the National League of Major League Baseball, especially focusing on the introduction of a relief pitcher in consideration with his handedness. [ABSTRACT FROM AUTHOR]

Markov models are commonly used in modelling many practical systems such as telecommunication systems, manufacturing systems and inventory systems. In this paper we propose a multivariate Markov chain model for modelling multiple categorical data sequences. We develop efficient estimation methods for the model parameters. We then apply the model and method to demand predictions for a soft-drink company in Hong Kong. [ABSTRACT FROM AUTHOR]

The context of planned preventive maintenance lends itself readily to probabilistic modelling. Indeed, many of the published theoretical models to be found in the literature adopt a Markov approach, where states are usually ‘operating’, ‘operating at one of several levels of deterioration’, and ‘failed’. However, most of these models assume the required Markovian property and do not address the issue of testing the assumption, or the related task of estimating parameters. It is possible that data are inadequate to test the assumption, or that the Markov property is believed to be not strictly valid, but acceptable as an approximation. In this paper we consider within a specific inspection–maintenance context the robustness of a Markov‐based model when the Markov assumption is not valid. This is achieved by comparing the output of an exact delay time model of an inspection–maintenance problem with that of a semi‐Markov approximation. The importance of establishing the vadility of the Markov property in the modelling application is highlighted. If the plant behaviour is seen to be nearly Markov, in the case considered the semi‐Markov model gives a good approximation to the exact model. Conversley if the Markov assumption is not a good approximation, the semi‐Markov model can lead to inappropriate advice. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the pricing of convertible bonds on a single underlying asset with dividend yield in a regime-switching economy. The dynamics of the risky asset are assumed to follow a Markov-modulated geometric Brownian motion. That is, the market parameters, such as the market interest rate, dividend yield and the volatility of the underlying risky asset, depend on unobservable states of the economy that are modelled by a continuous-time hidden Markov process. By means of the homotopy analysis method, an analytic formula for pricing convertible bonds with dividend yield in a two-state regime-switching model is presented. [ABSTRACT FROM AUTHOR]

This paper considers the problem of condition-based maintenance optimization for complex industrial assets involving load sharing interaction and fault propagation among their components using a two tiered approach. The upper layer represents the deterioration and failure at the asset level and uses a continuous-time Markov chain to calculate the optimal inspection interval and maintenance threshold. The lower layer models the load sharing interaction and fault propagation, and in turn calculates the deterioration rates and failure rates to be used in the upper layer. We derive a partitioning rule to transform the lower layer model into the upper layer model's format. Hence, we are able to reduce the size of state space and circumvent the state space explosion problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the use of some representation results for double martingales to value and hedge contingent claims in a Markovian regime-switching market. A set of N Markov jump assets is introduced to complete the Markovian regime-switching market. Using a representation for double martingales, we justify the completeness of the enlarged market. An equivalent martingale measure, or price kernel, in the enlarged market is then identified by a measure change. The option pricing formula and the hedging portfolio in the enlarged market is also discussed. [ABSTRACT FROM AUTHOR]

Sequential pattern mining has been a popular data mining technique for extracting useful information from large databases and has successfully been used for numerous industrial and commercial problems. This paper presents a new mathematical modelling application to healthcare, providing important information to health service managers and policy makers to help them identify sequential patterns which require attention for efficiently managing scarce healthcare resources and developing effective healthcare management policies. In healthcare, these sequential patterns are analogous to the patient pathways. We present a non-homogeneous Markov model for identifying not only patient pathways which have high probability but also for identifying pathways which incur high cost or time. In order to have a more realistic model, we also consider time-dependent covariates and their impact on the pathways. An algorithm based on branch and bound global optimization is presented which can efficiently extract a required number of such patient pathways of interest. The approach is illustrated using historical data on geriatric patients from an administrative database of a London hospital. [ABSTRACT FROM PUBLISHER]

We consider the problem of modelling processes sequentially changing behaviour and unexpected changes that can hinder finding the best approximation function. These dynamics cannot be observed directly either because they are masked by observational noise or because the process generating them is too complex and involves too many variables. In this paper, the problem of modelling financial time series has been approached using hidden Markov models (HMMs), which have been shown to be suitable for sequential data analysis and in particular for financial time series modelling and forecasting. HMMs are essentially data-driven models that allow us to focus attention on the observation generation process, which is indeed final objective. The goal of our time series analysis model is the generation of scenarios to be included in decision models. Therefore, our focus will not be on determining the best forecast but in capturing the generation process behaviour in order to characterize its possible evolutions. [ABSTRACT FROM AUTHOR]

In this paper are analysed the length of service and age characteristics of members in a hierarchical organization under the influence of `proportionality' policies. Proportionality policies are those that restrict the recruitment to every level of the hierarchy to be in strict proportion to the promotions into that level. The characteristics of the length of service in grade as well as those of the length of service in organization under these conditions have been derived. The characteristics of the chronological age of the members in the organization have also been derived. The analyses will be of relevance to organizations which outsource a part of their work, the outsourced workforce being notionally viewed as recruits to the system. [ABSTRACT FROM AUTHOR]

In this paper we propose a methodology for measuring the ‘relative effectiveness’ of healthcare services (i.e. the effect of hospital care on patients) under general conditions, in which: 6) a healthcare outcome underlies qualitative and quantitative observable indicators; β) we are interested in studying the simultaneous dependency of multiple outcomes on covariates (where the outcomes can also be correlated to each other); γ) the relative effectiveness is adjusted for hospital-specific covariates; 8) we hypothesise a general distribution for random disturbances and the random parameters of relative effectiveness. For this topic, a generalisation of the SURE (seemingly unrelated regression equations) multilevel model is proposed. The solutions are obtained by means of Bayesian inference methods. Since there is currently no software available to estimate this model, an SAS procedure based on Markov Chain Monte Carlo methods has been developed by the authors, in line with Goldstein & Spiegelhalter (1996, .L R. Stat. Soc. Set A, 159, 385–443), Spiegelhalter et al. (1996, Bayesian Using Gibbs Sampling Manual. Cambridge: MRC Bio-statistic Unit, Institute of Public Health) and Albert & Chib (1997, J. Am. Stat. Assoc., 92, 916–925). In addition, a new theoretical result regarding the joint posterior distribution for the parameters is provided. The model proposed has been implemented for an effectiveness study of a selection of Lombard hospitals. [ABSTRACT FROM AUTHOR]

This paper deals with component commonality in start-up manufacturing firms. We present a two-product Markov decision model that examines the implications of the inventory and production strategies for the survival probability of the firm. The advantage of using component commonality is studied for varying costs, demand correlations and order replenishment lead times. Optimal policies are derived, and minimum stock levels for survival are obtained. Moreover, we state the conditions under which simplified production decisions can be made. It is shown that commonality is not only useful as a way of dealing with demand uncertainty, but that its increased use is preferred for strongly substitutable products, and shorter replenishment lead times. [ABSTRACT FROM AUTHOR]

A common problem that faces many high-tech electronic product companies is how to effectively provide systems support for their products/machines/systems installed at various customer sites using different levels of technical personnel. The problem can be viewed as a model with multiple level servers and multiple volume demands. In this paper, a semi-Markov decision process with average criterion has been employed to formulate the dynamics of the system. Optimal policies for human resource allocation decision with minimum costs have been derived and the loss rate for customer requests has been considered. We prove that the embedding Markov chain is ergodic, induced by any stationary deterministic policy. We obtain some related parameters which can answer questions from managers. We also provide some numerical examples. [ABSTRACT FROM AUTHOR]

This paper discusses the use of dynamic modelling in consumer credit risk assessment. It surveys the approaches and objectives of behavioural scoring, customer scoring and profit scoring. It then investigates how Markov chain stochastic processes can be used to model the dynamics of the delinquency status and behavioural scores of consumers. It discusses the use of segmentation, mover–stayer models and the use of second‐ and third‐order models to improve the fit of such models. The alternative survival analysis proportional hazards approach to estimating when default occurs is considered. Comparisons are made between the ways credit risk is modelled in consumer lending and corporate lending. [ABSTRACT FROM PUBLISHER]

This study models soccer as a Markov process. We discretize the pitch into nine zones, and define the states of the Markov process according to the zone of the pitch in which the ball is located, the team in possession and the score. Log-linear models are used to represent state transitions. Using the log-linear models, we estimate team strengths not only with respect to scoring or conceding, but also with respect to gaining or losing possession, while considering the discretized zones in which the ball is located. We use play-by-play data from Japan League Division 1 games in the 2015 season to illustrate our approach, and characterize the strengths of teams in this league. Sanfrecce Hiroshima is used as a particular example. We determine the goodness-of-fit of the log-linear models. Additionally, we introduce random effects into the log-linear models and discuss the complexity of the state transition process. We demonstrate that our Markov model, at the nine-zone level, provides estimates of teams' strengths to a good approximation. [ABSTRACT FROM AUTHOR]

Hospitals are currently facing nigh incidences of ambulance bypass, long waiting lists for elective procedures and a significant proportion of patients experiencing long stays in the emergency department before moving to a bed in a ward. We observe that the system of wards and the emergency department in essence operates on two time-scales: the wards operate on a time-scale of days, whereas the state of the emergency department evolves on a much faster time-scale. This observation has motivated us to construct a two-time-scale model for a hospital system. The faster time-scale is modelled by a continuous time Markov chain, whereas the slower time-scale (ward occupancy) is modelled by a discrete time Markov chain. Given the nature of the system, the state of the wards has a direct impact on the emergency department. [ABSTRACT FROM AUTHOR]

An interest rate process assumed as a function of a continuous-time finite-state Markov chain representing the 'state of economy' is considered. Within this framework, the dynamics of the expected value of the Markov chain process under the forward measure are calculated and used to obtain explicit expressions for the price of bond options, caps, floors and cap yields. [ABSTRACT FROM AUTHOR]

In recent years, data-driven approaches have become a popular tool in a variety of sports to gain an advantage by, for example, analysing potential strategies of opponents. Whereas the availability of play-by-play or player tracking data in sports such as basketball and baseball has led to an increase of sports analytics studies, equivalent data sets for the National Football League (NFL) were not freely available for a long time. In this contribution, we consider a comprehensive play-by-play NFL dataset provided by www.kaggle.com , comprising 289,191 observations in total, to predict play calls in the NFL using hidden Markov models. The resulting out-of-sample prediction accuracy for the 2018 NFL season is 71.6%, which is similar compared to existing studies on play call predictions in the NFL. In practice, such predictions are helpful for NFL teams, especially for defense coordinators, to make adjustments in real time on the field. [ABSTRACT FROM AUTHOR]

We develop a reduced-form credit risk model with regime-switching intensities to investigate the pricing of a credit default swap (CDS) contract. We assume that the defaults of all the names are driven by some shock events. The arrivals of the shock events and the interest rate are modelled by a multivariate regime-switching shot noise process. We provide the flexibility that the model parameters, including the intensities and the jump sizes of the jump component, can switch over time according to a continuous-time, finite-state Markov chain. The states of the chain may be interpreted as different states of an economy or different stages of a business cycle. Based on the joint Laplace transform of the regime-switching shot noise processes, we derive the explicit formulas for the spreads of CDS contract with and without counterparty risk. Numerical results illustrate changes of market regimes have a significant effect on the spread. [ABSTRACT FROM AUTHOR]

In this article, we discuss the pricing of dynamic fund protection when the value process of the investment fund is governed by a geometric Brownian motion with parameters modulated by a continuous-time, finite-state hidden Markov chain. Under a risk-neutral probability measure, selected by the Esscher transform, we adopt the partial differential equation approach to value the dynamic fund protection. Using the estimated sequence of the hidden Markov chain, we apply the Baum-Welch algorithm and the Viterbi algorithm to derive the maximum likelihood estimates of the parameters. Numerical examples are provided to illustrate the practical implementation of the model. [ABSTRACT FROM AUTHOR]

We propose an efficient hybrid tree/finite difference method in order to approximate the Heston model (and possibly other stochastic volatility models). We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the approximation of European and American option prices. We finally provide numerical experiments that give accurate option prices in the Heston model, showing the reliability and the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

We propose a switching regression model for hedge funds to capture the characteristics of trading strategies through time. The coefficients are governed by a discrete-time Markov chain and are able to switch between regimes. The states of the Markov chain represent different states of the economy. Hedge fund indices from main trading strategies and market indices are chosen as regressors. A filtering technique by Elliott (1994, Exact adaptive filters for Markov chains observed in Gaussian noise. Automatica, 30, 1399–1408) is used to filter out hidden information and optimal parameter estimates are derived through a filter-based Expectation–Maximization algorithm. Our switching regression model is applied to individual hedge fund series from the Hedge Fund Research database. [ABSTRACT FROM PUBLISHER]

Open pipeline order fulfilment systems have emerged in sectors such as the automotive industry that offer a large number of product variants to the marketplace. In an open pipeline a customer can be fulfilled from anywhere in the system—by a stock product, by a product in the distribution system, by allocating a product in production or a product in the plan, or by supplying a product specially built to order (BTO). Here new results are presented to estimate the performance metrics for open pipeline systems. An exact expression is developed based on a Markov analysis to calculate the BTO proportion for any combination of the key system parameters—pipeline length, the variety level and the initial stock level. Approximation schemes are developed to estimate the pipeline and stock fulfilment proportions, the mean lead time and the mean stock level. The approximation schemes provide accurate estimates for a large range of systems. Specific issues that affect the estimation of performance metrics in low variety, open pipeline systems are discussed. The results presented provide generic insights for open pipeline systems design and management and provide a platform for further work in extending the applicability of open pipeline concepts. [ABSTRACT FROM AUTHOR]

The Ryder Cup is played for between the golfers of Europe and the USA and consists of 8 foursomes, 8 fourballs and 12 singles matches played over 3 days. Each match is worth one point; hence, to win, a team must gain at least W/i points. In live coverage of the event, considerable attention is paid to the predicted outcome but typically this is assessed by the crude method of assuming that any match a team is currently leading is worth one point and any match currently level is worth Vi point. No distinction is made between a match where a team is one up after one hole and one where it is eight up with nine to play. A Markovian model provides a more well-informed prediction of the outcome, in terms of the expected number of points to be won by each team given the current score in each match. This takes account of estimates of the probabilities of holes being won or halved in the different formats of fourballs, foursomes and singles, based on historical data from the Ryder Cup and other major professional golf tournaments. As well as an expected final score, the model also provides a probability distribution of the event outcome and could be used to estimate the implicit odds of any outcome for 'in-play' betting. [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]

Many financial decision problems require scenarios for multivariate financial time series that capture their sequentially changing behaviour, including their extreme movements. We consider modelling financial time series by hidden Markov models (HMMs), which are regime-switching-type models. Estimating the parameters of an HMM is a difficult task and the multivariate case can pose serious implementation issues. After the parameter estimation, the calibrated model can be used as a scenario generator to describe the future realizations of asset prices. The scenario generator is tested in a single-period mean–conditional value-at-risk optimization problem for portfolio selection. [ABSTRACT FROM PUBLISHER]

The impact of a preventive rating maintenance policy on the rating process is investigated through the definition of a semi-Markov maintenance model with imperfect repair at random times. The results allow us to study the rating migrations process in the transient and the asymptotic case. [ABSTRACT FROM AUTHOR]

The Maximum Likelihood estimator is used within a lognormal diffusion process and closed form analytical solutions are obtained. The monthly CPJ forecasts are estimated for the period between 1970 and 2002. The quarterly estimates of inflation rates are obtained from monthly forecasts rather than from quarterly data. This has significantly improved the estimates of inflation rates. The model also produced a superior fit as compared to random walk and GARCH(p,q)-M models. The adopted approach is found to be simple, economical and generally suitable for modelling stochastic processes that reflect aggregation over time stemming from many factors, and in which the transition path between consecutive states is relatively smooth. [ABSTRACT FROM AUTHOR]

Hidden Markov models (HMMs) are widely used in science, engineering and many other areas. In a HMM, there are two types of states: hidden states and observable states. Here we propose a HMM via the framework of a Markov chain model. Simple estimation methods for the transition probabilities among the hidden states are discussed. The estimation methods are better than the traditional EM algorithm in both the quality of estimation and the computational complexity. We then apply the model to classify the customers of a computer service company which is an important task in the customer relationship management. Numerical examples are given to illustrate the usefulness of the model by using a real-world data set. [ABSTRACT FROM AUTHOR]

The basic principle of total productive maintenance (TPM) is to reduce and ultimately eliminate breakdowns by pre‐emptive maintenance strategies, which rely on the cooperation of all employees. When properly applied, TPM can bring about tremendous improvements in a company's performance. However, recent research, using interviews and questionnaires, suggests that many managers in manufacturing industries in Europe still have to be convinced of the usefulness of TPM. Many more are perhaps unsure of the losses which can accrue as a consequence of not having an appropriate maintenance programme implemented in their organizations. A simple yet powerful Markov model is proposed as a diagnostic tool for the manager who wants an effective way of identifying the prime costs involved in production line downtimes, and hence the potential benefits of TPM. The influence of the performance of a single machine on a line can be investigated. This is vital information for strategic planning of machine replacements, which involve major capital investments. In particular, an approximate analysis of the benefits of a machine building up a buffer stock is presented, and assessed against the costs involved. The model has been implemented as an Excel macro. [ABSTRACT FROM PUBLISHER]