On stochastic processes with linear conditional moments

In the paper, we show that a stochastic process with linear regression and linear conditional variance must be either a Gaussian process or a Poisson-type process. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

On augmented Lagrangian decomposition methods for multistage stochastic programs

A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented.     

On simple stochastic diffusion models

This paper expands the diffusion of information models developed by Funkhouser and McCombs (1972) to include situations involving simple interaction processes and more complicated situations involving both mass mediated messages and interactively mediated messages. This paper develops discrete time models of information diffusion as opposed to the continuous time models developed by Coleman (1964) and Bartholomew (1967) and others.     

On stochastic models of teletraffic with heavy-tailed distributions

Following the approach suggested by I. Kaj and M. Taqqu, we consider a stochastic model of teletraffic based on Poisson random measure. We show that under appropriate assumptions, the finite-dimensional distributions for the scaled workload process converge to those of a stable Lévy process. Bibliography: 10 titles.     

Some stochastic comparisons of conditional coherent systems

This paper investigates coherent systems with independent and identical components. Stochastic comparison on the residual life and the inactivity time of two systems with stochastically ordered signatures is conducted. Copyright © 2008 John Wiley & Sons, Ltd.     

On a class of stochastic models with two-sided jumps

In this paper a stochastic process involving two-sided jumps and a continuous downward drift is studied. In the context of ruin theory, the model can be interpreted as the surplus process of a business enterprise which is subject to constant expense rate over time along with random gains and losses. On the other hand, such a stochastic process can also be viewed as a queueing system with instantaneous work removals (or negative customers). The key quantity of our interest pertaining to the above model is (a variant of) the Gerber–Shiu expected discounted penalty function (Gerber and Shiu in N. Am. Actuar. J. 2(1):48–72, 1998) from ruin theory context. With the distributions of the jump sizes and their inter-arrival times left arbitrary, the general structure of the Gerber–Shiu function is studied via an underlying ladder height structure and the use of defective renewal equations. The components involved in the defective renewal equations are explicitly identified when the upward jumps follow a combination of exponentials. Applications of the Gerber–Shiu function are illustrated in finding (i) the Laplace transforms of the time of ruin, the time of recovery and the duration of first negative surplus in the ruin context; (ii) the joint Laplace transform of the busy period and the subsequent idle period in the queueing context; and (iii) the expected total discounted reward for a continuous payment stream payable during idle periods in a queue.     

On input-to-state stability for stochastic multi-group models with multi-dispersal

This paper focuses on the input-to-state stability for a general class of stochastic multi-group models with multi-dispersal. By incorporating graph theory with Lyapunov method as well as stochastic analysis techniques, novel sufficient criteria are derived, which are in the form of Lyapunov-type theorem and coefficient-type criterion, respectively. Moreover, to show the applicability of our findings, we employ coefficient-type criterion to analyze the input-to-state stability for stochastic coupled oscillators. Finally, a numerical example and its simulations are offered to demonstrate the validity and feasibility of the theoretic results.     

About conditional masking probability models

We study the existing models for right-censored competing risks data and with masked failure cause. By introducing a new random variable hidden behind the current models, we give a practical interpretation of the symmetry assumption made by almost all researchers in this field. We further point out that the drawback of the symmetry assumption is that it has a strong restriction on the underlying distribution function to be studied. Moreover, we correct an assumption in the current models.     

Asymptotic theory of conditional inference for stochastic processes

This paper develops an approach to conditional inference for nonergodic stochastic process models by considering asymptotic properties. The context for most of the analysis is that of Le Cam's local asymptotic theory: in particular, the locally asymptotically mixed normal (LAMN) situation. An attempt has been made to evaluate local asymptotic properties of global procedures.     

On relations between DEA-risk models and stochastic dominance efficiency tests

In this paper, several concepts of portfolio efficiency testing are compared, based either on data envelopment analysis (DEA) or the second-order stochastic dominance (SSD) relation: constant return to scale DEA models, variable return to scale (VRS) DEA models, diversification-consistent DEA models, pairwise SSD efficiency tests, convex SSD efficiency tests and full SSD portfolio efficiency tests. Especially, the equivalence between VRS DEA model with binary weights and the SSD pairwise efficiency test is proved. DEA models equivalent to convex SSD efficiency tests and full SSD portfolio efficiency tests are also formulated. In the empirical application, the efficiency testing of 48 US representative industry portfolios using all considered DEA models and SSD tests is presented. The obtained efficiency sets are compared. A special attention is paid to the case of small number of the inputs and outputs. It is empirically shown that DEA models equivalent either to the convex SSD test or to the SSD portfolio efficiency test work well even with quite small number of inputs and outputs. However, the reduced VRS DEA model with binary weights is not able to identify all the pairwise SSD efficient portfolios.     

Bayesian analysis of conditional autoregressive models

Conditional autoregressive (CAR) models have been extensively used for the analysis of spatial data in diverse areas, such as demography, economy, epidemiology and geography, as models for both latent and observed variables. In the latter case, the most common inferential method has been maximum likelihood, and the Bayesian approach has not been used much. This work proposes default (automatic) Bayesian analyses of CAR models. Two versions of Jeffreys prior, the independence Jeffreys and Jeffreys-rule priors, are derived for the parameters of CAR models and properties of the priors and resulting posterior distributions are obtained. The two priors and their respective posteriors are compared based on simulated data. Also, frequentist properties of inferences based on maximum likelihood are compared with those based on the Jeffreys priors and the uniform prior. Finally, the proposed Bayesian analysis is illustrated by fitting a CAR model to a phosphate dataset from an archaeological region.     

Diagnostic checking for conditional heteroscedasticity models

We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series. The tests can detect the alternatives converging to the null at a parametric rate. Weight functions are involved in the construction of the tests, which provides us with the flexibility to choose scores, especially under directional alternatives, for enhancing power performance. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. A simulation study is carried out and a real data is analyzed.     

Multivariate probit models for conditional claim-types

This paper considers statistical modeling of the types of claim in a portfolio of insurance policies. For some classes of insurance contracts, in a particular period, it is possible to have a record of whether or not there is a claim on the policy, the types of claims made on the policy, and the amount of claims arising from each of the types. A typical example is automobile insurance where in the event of a claim, we are able to observe the amounts that arise from say injury to oneself, damage to one’s own property, damage to a third party’s property, and injury to a third party. Modeling the frequency and the severity components of the claims can be handled using traditional actuarial procedures. However, modeling the claim-type component is less known and in this paper, we recommend analyzing the distribution of these claim-types using multivariate probit models, which can be viewed as latent variable threshold models for the analysis of multivariate binary data. A recent article by Valdez and Frees [Valdez, E.A., Frees, E.W., Longitudinal modeling of Singapore motor insurance. University of New South Wales and the University of Wisconsin-Madison. Working Paper. Dated 28 December 2005, available from: http://wwwdocs.fce.unsw.edu.au/actuarial/research/papers/2006/Valdez-Frees-2005.pdf] considered this decomposition to extend the traditional model by including the conditional claim-type component, and proposed the multinomial logit model to empirically estimate this component. However, it is well known in the literature that this type of model assumes independence across the different outcomes. We investigate the appropriateness of fitting a multivariate probit model to the conditional claim-type component in which the outcomes may in fact be correlated, with possible inclusion of important covariates. Our estimation results show that when the outcomes are correlated, the multinomial logit model produces substantially different predictions relative to the true predictions; and second, through a simulation analysis, we find that even in ideal conditions under which the outcomes are independent, multinomial logit is still a poor approximation to the true underlying outcome probabilities relative to the multivariate probit model. The results of this paper serve to highlight the trade-off between tractability and flexibility when choosing the appropriate model.     

On confined McKean Langevin processes satisfying the mean no-permeability boundary condition

We construct a confined Langevin type process aimed to satisfy a mean no-permeability condition at the boundary. This Langevin process lies in the class of conditional McKean Lagrangian stochastic models studied by Bossy, Jabir and Talay (2010) [5]. The confined process considered here is a first construction of solutions to the class of Lagrangian stochastic equations with boundary condition issued by the so-called PDF methods for Computational Fluid Dynamics. We prove the well-posedness of the confined system when the state space of the Langevin process is a half-space.     

Discrete stochastic location models

In this paper, we study how the two classical location models, the simple plant location problem and thep-median problem, are transformed in a two-stage stochastic program with recourse when uncertainty on demands, variable production and transportation costs, and selling prices is introduced. We also discuss the relation between the stochastic version of the SPLP and the stochastic version of thep-median.     

On justification of use of stochastic functions for multimodal optimization models

A model of a complicated function under uncertainty is constructed axiomatically, formalizing suppositions on rationality of information on a considered function.