For two components in series and one redundancy with their lifetimes following the proportional hazard models, we build the likelihood ratio order and the hazard rate order for lifetimes of the redundant systems. Also, for ** k**-out-of-

This paper quantifies the asymptotic behavior of sample arc lengths in a multivariate time series. Arc length is a natural measure of the fluctuations in a data series and can be used to quantify volatility. The idea is that processes with larger sample arc lengths exhibit larger fluctuations and hence suggest greater volatility. Here, a Gaussian functional central limit theorem for sample arc lengths is proven under finite second moment conditions. With equally spaced observations, the theory is shown to apply when the first differences of the series obey many of the popular stationary time series models in today's literature, including autoregressive moving-average, generalized autoregressive conditional heteroscedastic, and stochastic volatility model classes. A cumulative sum statistic is introduced to identify series regimes of differing volatilities. Our applications consider log prices of asset series. Specifically, the results are used to detect nonstationary periods of stock prices. Copyright © 2014 John Wiley & Sons, Ltd.

This paper presents a queue-length analysis of ** Geo** ∕

We propose a numerical method to evaluate the performance of the emerging Generalized Shiryaev–Roberts (GSR) change-point detection procedure in a ‘minimax-ish’ multi-cyclic setup where the procedure of choice is applied repetitively (cyclically), and the change is assumed to take place at an unknown time moment in a distant-future stationary regime. Specifically, the proposed method is based on the integral-equations approach and uses the collocation technique with the basis functions chosen so as to exploit a certain change-of-measure identity and the GSR detection statistic's unique martingale property. As a result, the method's accuracy and robustness improve, as does its efficiency as using the change-of-measure ploy the Average Run Length (ARL) to false alarm and the Stationary Average Detection Delay (STADD) are computed simultaneously. We show that the method's rate of convergence is quadratic and supply a tight upper bound on its error. We conclude with a case study and confirm experimentally that the proposed method's accuracy and rate of convergence are robust with respect to three factors: (a) partition fineness (coarse vs. fine), (b) change magnitude (faint vs. contrast), and (c) the level of the Average Run Length to false alarm (low vs. high). Because the method is designed not restricted to a particular data distribution or to a specific value of the GSR detection statistic's head start, this work may help gain greater insight into the characteristics of the GSR procedure and aid a practitioner to design the GSR procedure as needed while fully utilizing its potential. Copyright © 2014 John Wiley & Sons, Ltd.

]]>This paper proposes a condition-based maintenance policy for deteriorating units, which are to be considered failed when their wear exceeds a critical threshold level, even if this exceeding is not associated to a sudden breakdown of the unit but only to degraded performance. Thus, the failure occurrence can be detected only at periodic inspections. In such a framework, given the unit age and state at inspection, a decision-making rule is proposed to choose the maintenance action to be taken, in order to extend the used life of the unit without significantly increasing its failure probability, so to reduce the life cycle cost. Both the case when all inspection times are planned and the case when an additional maintenance can be scheduled before the next planned inspection are considered. An application to a real case study referring to the wearing process of cylinder liners of some marine diesel engines is illustrated, with the further aim of highlighting the need to correctly model the degradation process. Copyright © 2014 John Wiley & Sons, Ltd.

]]>Most of the methods developed for hydrothermal power system planning are based on scenario-based stochastic programming and therefore represent the stochastic hydro variable (water inflows) as a finite set of hydrological scenarios. As the level of detail in the models grows and the associated optimization problems become more complex, the need to reduce the number of scenarios without distorting the nature of the stochastic variable is arising. In this paper, we propose a scenario reduction method for discrete multivariate distributions based on transforming the moment-matching technique into a combinatorial optimization problem. The method is applied to hydro inflow data from the Chilean Central Interconnected System and is benchmarked against results for the optimal operation of the Chilean Central Interconnected System determined with the selected subsets and the complete set of historical hydrological scenarios. Simulation results show that the proposed scenario-reduction method could adequately approximate the probability distribution of the objective function of the operational planning problem. Copyright © 2014 John Wiley & Sons, Ltd.

This paper studies the criterion of local risk-minimization for life insurance contracts in a financial market, which includes longevity bonds. The longevity bond is a bond specifying payments, which are linked to the current number of survivors in a given portfolio of insured lives. The number of survivors is modeled via a double-stochastic process, where the mortality intensity is driven by a time-inhomogeneous Cox–Ingersoll–Ross model. In addition to the longevity bond, the financial market is assumed to consist of a traditional bond and a savings account. We define the price process of the longevity bond by introducing a pricing measure. The paper extends previous work in the literature to the case where the traded assets are not martingales under the measure used for determining the optimal strategies. We compare our results under the real measure with the former results of globally risk-minimizing strategies, obtained using an equivalent martingale measure. Copyright © 2014 John Wiley & Sons, Ltd.

We consider a finite-buffer queue where arrivals occur according to a batch Markovian arrival process (*BMAP*), and there are two servers present in the system. At the beginning of a busy period, the low performance server serves till queue length reaches a critical level , and when queue length is greater than or equal to *b*, the high performance server starts working. High performance server serves till queue length drops down to a satisfactory level *a *( < *b*) and then low performance server begins to serve again, and the process continues in this manner. The analysis has been carried out using a combination of embedded Markov chain and supplementary variable method. We obtain queue length distributions at pre-arrival-, arbitrary- and post-departure-epochs, and some important performance measures, such as probability of loss for the first-, an arbitrary- and the last-customer of a batch, mean queue length and mean waiting time. The total expected cost function per unit time is derived in order to determine locally optimal values for *N*, *a* and *b* at a minimum cost. Both partial- and total-batch rejection strategies have been analyzed. Also, we investigate the corresponding *BMAP* ∕ *G* − *G* ∕ 1 ∕ ∞ queue using matrix-analytic- and supplementary variable-method. We calculate previously described probabilities with performance measures for infinite-buffer model as well. In the end, some numerical results have been presented to show the effect of model parameters on the performance measures. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we describe the usefulness and the applications of the multivariate conditional hazard rate functions. First, we define these, as well as the accumulated hazard functions, and then give some properties of them. Using these definitions and properties, we describe the total hazard construction and its main traits. Using the technical tools described previously, we define and discuss various stochastic orders, various positive dependence concepts, and various aging notions that entail nonnegative multivariate random vectors. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, we design a supply chain finance system with a manufacturer, a retailer and a commercial bank where both the retailer and manufacturer are capital constrained under demand uncertainties. We formulate a bi-level Stackelberg game for the supply chain finance system in which the bank acts as the leader and the manufacturer as the subleader. Considering the bankruptcy risks of the manufacturer and the retailer, we analyze the optimal financing interest rate for the commercial bank, the optimal order for the retailer and the optimal wholesale price for the manufacturer, respectively. We compare our model with two benchmark cases, that is, no financing scheme and infinite-credit-line financing scheme, to find out the important interactions between the operational and financial decisions in the supply chain finance system. It concluded that the different interest rates and credit lines would affect the supply chain operations. Finally, we demonstrate the impacts of different capital levels and interest rates on the optimal decisions through numerical studies that validate our theoretical analysis. Copyright © 2014 John Wiley & Sons, Ltd.

For mission-critical or safety-critical systems, redundancy techniques are often applied to satisfy the stringent reliability requirements of the system design. Warm standby sparing is a common redundancy technique, which compromises the high energy consumption of hot standby techniques and the long recovery time of cold standby techniques. This paper considers a more general model for warm standby systems, that is, the demand-based warm standby system, where each component bears a nominal capacity and the system fails if the total capacity of the working components cannot meet the system demand. Moreover, fault level coverage is considered to model the imperfect coverage effect in the standby system. A multivalued decision diagram based approach is proposed to evaluate the reliability of the demand-based warm standby system subject to the fault level coverage. Examples are given to illustrate the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

A two-component system is considered, which is subject to accumulative deterioration. Because of common stress, the components are dependent. Their joint deterioration is modelled with a bivariate nondecreasing Lévy process. The deterioration level of both components is known only through perfect and periodic inspections. By an inspection, components with deterioration level beyond a specific threshold are instantaneously replaced by new ones (corrective or preventive replacements). Otherwise, they are left as they are. Between inspections, failures remain unrevealed. This replacement policy is classical in a univariate setting, with deterioration modelled by a Gamma process. In the bivariate case, it leads to imperfect repairs at the system level, which highly complicates the study. The replacement policy is assessed through cost functions on both finite and infinite horizons, which take into account some economical dependence between components. Markov renewal theory is used to study the behaviour of the system, in a continuous and bivariate setting. Numerical experiments illustrate the study, considering a specific Lévy process with univariate Gamma processes as margins. Although technical details are not provided here for the numerical computations, the paper shows that there is a technical gap between the traditional one-dimensional studies and the present two-dimensional one, especially for the computation of the asymptotic distribution of the underlying Markov chain. Hence, there is a need for further development in the bivariate (or multivariate) setting. Copyright © 2014 John Wiley & Sons, Ltd.

]]>This paper presents an autoregressive model for a finite sequence of random variables that are observed at points equally spaced on the unit circle. The proposed model is an extension of the well-known autoregressive model of time series. We demonstrate that this model amounts to a linear transformation of a vector of independent and identically distributed random variables. The second-order properties of the multivariate distribution were examined. The least squares estimators of the model parameters were obtained. The connection between the proposed first-order model and a second-order, stationary, mean-square-continuous, real-valued random process on the unit circle was considered. We used the model presented to describe the fluctuations of hoop residual stresses in the rims of new railroad wheels. The stress measurement was performed using an ultrasonic method. The stress fluctuation model allowed us to determine the number of measurement points required to assess residual stress levels in the wheels. Copyright © 2014 John Wiley & Sons, Ltd.

Based on a new multiscale hybrid structure of the volatility of the underlying asset price, we study the pricing of a European option in such a way that the resultant option price has a desirable correction to the Black–Scholes formula. The correction effects are obtained by asymptotic analysis based upon the Ornstein–Uhlenbeck diffusion that decorrelates rapidly while fluctuating on a fast time-scale. The subsequent implied volatilities demonstrate a smile effect (right geometry), which overcomes the major drawback of the Black–Scholes model as well as local volatility models, and move to a right direction as the underlying asset price increases (right dynamics), which fits the observed market behavior and removes the possible instability of hedging that the local volatility models may cope with. Further, we demonstrate that our correction brings significant improvement in terms of fitting to the implied volatility surface through a calibration exercise. Copyright © 2014 John Wiley & Sons, Ltd.

]]>The primary aim of this paper is to expose the use and the value of spatial statistical analysis in business and especially in designing economic policies in rural areas. Specifically, we aim to present under a unified framework, the use of both point and area-based methods, in order to analyze in-depth economic data, as well as, to drive conclusions through interpreting the analysis results. The motivating problem is related to the establishment of women-run enterprises in a rural area of Greece. Moreover, in this article, the spatial scan statistic is successfully applied to the spatial economic data at hand, in order to detect possible clusters of small women-run enterprises in a rural mountainous and disadvantaged region of Greece. Then, it is combined with Geographical Information System based on Local Indicator of Spatial Autocorrelation scan statistic for further exploring and interpreting the spatial patterns. The rejection of the random establishment of women-run enterprises and the interpretation of the clustering patterns are deemed necessary, in order to assist government in designing policies for rural development. Copyright © 2014 John Wiley & Sons, Ltd.

The variable annuity product has many desirable features for retirement saving purposes, such as stock-linked growth potential, protection against losses in the investment, and guarantees of minimum payout amount at annuitization. Therefore, it is of great interest to study this product for designing next generation retirement solutions. Policyholder behavior is one of the most important profit or loss factors for the variable annuity product, and insurance companies generally do not have sophisticated models at the current time. This paper will discuss a new approach using modern statistical learning techniques to model policyholder withdrawal behavior with promising results. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we establish closed-form formulas for key probabilistic properties of the cone-constrained optimal mean-variance strategy, in a continuous market model driven by a multidimensional Brownian motion and deterministic coefficients. In particular, we compute the probability to obtain to a point, during the investment horizon, where the accumulated wealth is large enough to be fully reinvested in the money market, and safely grow there to meet the investor's financial goal at terminal time. We conclude that the result of Li and Zhou [*Ann. Appl. Prob.*, v.16, pp.1751–1763, (2006)] in the unconstrained case carries over when conic constraints are present: the former probability is lower bounded by 80% no matter the market coefficients, trading constraints, and investment goal. We also compute the expected terminal wealth given that the investor's goal is underachieved, for both the mean-variance strategy and the aforementioned hybrid strategy where transfer to the money market occurs if it allows to safely achieve the goal. The former probabilities and expectations are also provided in the case where all risky assets held are liquidated if financial distress is encountered. These results provide investors with novel practical tools to support portfolio decision-making and analysis. Copyright © 2013 John Wiley & Sons, Ltd.

This article considers the modeling of count data time series with a finite range having extra-binomial variation. We propose a beta-binomial autoregressive model using the concept of random coefficient thinning. We discuss the stationarity conditions, derive the moments and autocovariance function and consider approaches for parameter estimation. Furthermore, we develop two new tests for detecting extra-binomial variation, and we derive the asymptotic distributions of the test statistics under the null hypothesis of a binomial autoregressive model. The size and power performance of the two tests are analyzed under various alternatives taken from a beta-binomial autoregressive model with Monte Carlo experiments. The article ends with a real-data example about the Harmonised Index of Consumer Prices of the European Union. Copyright © 2013 John Wiley & Sons, Ltd.

]]>Cure models represent an appealing tool when analyzing default time data where two groups of companies are supposed to coexist: those which could eventually experience a default (uncured) and those which could not develop an endpoint (cured). One of their most interesting properties is the possibility to distinguish among covariates exerting their influence on the probability of belonging to the populations’ uncured fraction, from those affecting the default time distribution. This feature allows a separate analysis of the two dimensions of the default risk: *whether* the default can occur and *when* it will occur, given that it can occur. Basing our analysis on a large sample of Italian firms, the probability of being uncured is here estimated with a binary logit regression, whereas a discrete time version of a Cox's proportional hazards approach is used to model the time distribution of defaults. The extension of the cure model as a forecasting framework is then accomplished by replacing the discrete time baseline function with an appropriate time-varying system level covariate, able to capture the underlying macroeconomic cycle. We propose a holdout sample procedure to test the classification power of the cure model. When compared with a single-period logit regression and a standard duration analysis approach, the cure model has proven to be more reliable in terms of the overall predictive performance. Copyright © 2013 John Wiley & Sons, Ltd.

This paper deals with pricing a contract under which a dealer buys back a car from a client, for a cash amount contained in a given depreciation table. The value of the car is supposed to depreciate according to a stochastic model with random repairs modeled by a Poisson process. Copyright © 2013 John Wiley & Sons, Ltd.

]]>In this paper, we consider a classical risk process with dependence and in the presence of a constant dividend barrier. The dependence structure between the claim amounts and the interclaim times is introduced through a Farlie–Gumbel–Morgenstern copula. We analyze the expectation of the discounted penalty function and the expectation of the present value of the distributed dividends. For each function, an integro-differential equation with boundary conditions is derived, and the solution is provided. Finally, we find an explicit solution for each function when the claim amounts are exponentially distributed. We illustrate the impact of the dependence on these two quantities. Copyright © 2012 John Wiley & Sons, Ltd.

]]>To represent the high concentration of recovery rates at the boundaries, we propose to consider the recovery rate as a mixed random variable, obtained as the mixture of a Bernoulli random variable and a beta random variable. We suggest to estimate the mixture weights and the Bernoulli parameter by two logistic regression models. For the recovery rates belonging to the interval (0,1), we model, jointly, the mean and the dispersion by using two link functions, so we propose the joint beta regression model that accommodates skewness and heteroscedastic errors. This methodological proposal is applied to a comprehensive survey on loan recovery process of Italian banks. In the regression model, we include some macroeconomic variables because they are relevant to explain the recovery rate and allow to estimate it in downturn conditions, as Basel II requires. Copyright © 2012 John Wiley & Sons, Ltd.

]]>In industrial statistics, there is great interest in predicting with precision lifetimes of specimens that operate under stress. For example, a bad estimation of the lower percentiles of a life distribution can produce significant monetary losses to organizations due to an excessive amount of warranty claims. The Birnbaum–Saunders distribution is useful for modeling lifetime data. This is because such a distribution allows us to relate the total time until the failure occurs to some type of cumulative damage produced by stress. In this paper, we propose a methodology for detecting influence of atypical data in accelerated life models on the basis of the Birnbaum–Saunders distribution. The methodology developed in this study should be considered in the design of structures and in the prediction of warranty claims. We conclude this work with an application of the proposed methodology on the basis of real fatigue life data, which illustrates its importance in a warranty claim problem. Copyright © 2012 John Wiley & Sons, Ltd.

]]>A fundamental problem in financial trading is the correct and timely identification of turning points in stock value series. This detection enables to perform profitable investment decisions, such as buying-at-low and selling-at-high. This paper evaluates the ability of sequential smoothing methods to detect turning points in financial time series. The novel idea is to select smoothing and alarm coefficients on the gain performance of the trading strategy. Application to real data shows that recursive smoothers outperform two-sided filters at the out-of-sample level. Copyright © 2012 John Wiley & Sons, Ltd.

]]>In this paper, we consider the modeling and the inference of abandonment behavior in call centers. We present several time to event modeling strategies, develop Bayesian inference for posterior and predictive analyses, and discuss implications on call center staffing. Different family of distributions, piecewise time to abandonment models, and mixture models are introduced, and their posterior analysis with censored abandonment data is carried out using Markov chain Monte Carlo methods. We illustrate the implementation of the proposed models using real call center data, present additional insights that can be obtained from the Bayesian analysis, and discuss implications for different customer profiles. Copyright © 2012 John Wiley & Sons, Ltd.

]]>In this paper, we study the absolute ruin probability in the compound Poisson model with credit and debit interests and liquid reserves. At first, we derive a system of integro-differential equations with certain boundary conditions for the Gerber–Shiu function. Then, applying these results, we obtain asymptotical formula of the absolute ruin probability for subexponentially claims. Furthermore, when the claims are exponentially distributed, we obtain the explicit expressions for the Gerber–Shiu function and the exact solution for the absolute ruin probability. Finally, we discuss the absolute ruin probability by using the Gerber–Shiu function when debit interest is varying. In the case of exponential individual claim, we give the explicit expressions for the Gerber–Shiu function. Copyright © 2012 John Wiley & Sons, Ltd.

]]>In this paper, we consider the classical risk model modified in two different ways by the inclusion of a dividend barrier. For Model I, we present numerical algorithms, which can be used to approximate or bound the expected discounted value of dividends up to a finite time horizon, *t*, or ruin if this occurs earlier. We extend this by requiring the shareholders to provide the initial capital and to pay the deficit at ruin each time it occurs so that the process then continues after ruin up to time *t*. For Model I, we assume the full premium income is paid as dividends whenever the surplus exceeds a set level.

In our Model II, we assume dividends are paid at a rate less than the rate of premium income. Copyright © 2012 John Wiley & Sons, Ltd.

A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (*p*,*q*) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e-markets poses some specific challenges. The large amount of real-time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high-frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair-copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair-copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine-based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.

The development of optimal control strategies for many stochastic models relies on the observed traffic intensity. However, implementation of such control strategies is often infeasible because of high operating costs induced by the fluctuations of traffic flows. In this study, we propose a framework for estimating and monitoring the traffic intensities of stochastic systems. The framework does not require knowledge of any input traffic statistics, and it allows us to adaptively estimate the intensity function over time and simultaneously detect its significant changes so that the control strategy can be adjusted accordingly without requiring high operating costs. Finally, a canonical queueing system with various types of input traffic is used to evaluate the effectiveness of the proposed framework. Copyright © 2012 John Wiley & Sons, Ltd.

]]>In this paper, we consider a repairable system with minimal repairs whose number of repairs is a positive random variable with a given probability vector. Some preservation theorems and aging properties of repairable systems are established. Under the condition that at time *t* the system is working, a new random variable for the residual lifetime of the system is proposed. Some stochastic ordering results among the lifetimes and residual lifetimes of two systems are obtained. Similar results for coherent systems with independent components and exchangeable components were obtained in the previous literature. Copyright © 2013 John Wiley & Sons, Ltd.