Portfolio optimization of credit risky bonds: a semi-Markov process approach

This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds.The criteria to optimize the credit portfolio is based on l_(∞)-norm risk measure and the proposed optimization model is formulated as a linear programming problem.The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process.Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models,i.e.,it addresses the ageing effect present in the credit rating dynamics.The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds.The empirical performance of the proposed model is analyzed using the real data.Further,comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

Description and analysis of non-stationary signals by nested semi-Markov processes

The possibility of describing the time-dependent processes of scattering by underlying surfaces and the clear sky, as well as the seasonal behaviour of the refractive index of troposphere by using nested semi-Markov processes has been consid- ered. Local Gaussian models can be used to describe the process inside each phase state. The possibility of describing the sta- tistics of reflections from the sea and the refractive index by using Kravchenko finite functions has been shown for the first time.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

基于UGF和Semi-Markov方法的反应堆泵机组多状态可靠性分析

将通用发生函数(UGF)与半马尔可夫过程(Semi-Markov Process)相结合,对反应堆泵机组进行多状态可靠性分析。给出多状态系统可靠性分析的UGF算法模型,推导多状态设备性能状态的Semi-Markov过程概率表达式,定义设备、系统性能值的定量描述方法。以性能参数是否满足需求值做为系统成功与失效的判据,对比分析反应堆泵机组在需求性能条件下的多状态可用度与2状态可用度结果,并给出系统在任务周期内的平均性能值。结果表明,该方法能够定量分析部分失效对系统可靠性的影响,降低传统的2态可靠性分析方法产生的不必要的保守程度。

Reliability Evaluation of Two-Stage Directed Semi-Markov Repairable Network Systems

A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.

Semi-Markovian Model of Two-Line Queuing System with Losses

In the present paper, to build model of two-line queuing system with losses GI/G/2/0, the approach introduced by V.S. Korolyuk and A.F. Turbin, is used. It is based on application of the theory of semi-Markov processes with arbitrary phase space of states. This approach allows us to omit some restrictions. The stationary characteristics of the system have been defined, assuming that the incoming flow of requests and their service times have distributions of general form. The particular cases of the system were considered. The used approach can be useful for modeling systems of various purposes.

The Use of Analytic Hierarchy Process （AHP） in the Determination of Earnings Quality： The Case of UAE

The purpose of this study is to review and demonstrate how analytic hierarchy process （AHP） can be employed to determine earnings quality. The AHP technique can make the analysis studies more effective, easy, and applicable to companies to calculate the relative weights of each dimension, sub-dimension, and specific sub-dimension of earnings quality. A common understanding of earnings quality is difficult to define and even more difficult to measure precisely. In addition to this, the earnings quality is influenced by factors which are often intangible and immeasurable and, as such, when assessing earnings quality, judgments will be largely subjective. Further, earnings quality is related to business concepts or practices and affected by other factors such as the nature and source of earnings. In relation to this, earnings quality would be directly influenced by the conservatism of the chosen methods. However, earnings quality relates to the persistence of earnings and to the likelihood of cash realization on reported eamings. Overall, the results presented from the paramorphic model under AHP are meant to be descriptive of the decision process of five investment analysts within three different companies. The results in this study offer valuable insights into how a small population of investment analysts actually decides the relative importance of various earnings quality dimensions.

Remaining useful life prediction for engineering systems under dynamic operational conditions: A semi-Markov decision process-based approach

For critical engineering systems such as aircraft and aerospace vehicles, accurate Remaining Useful Life(RUL) prediction not only means cost saving, but more importantly, is of great significance in ensuring system reliability and preventing disaster. RUL is affected not only by a system's intrinsic deterioration, but also by the operational conditions under which the system is operating. This paper proposes an RUL prediction approach to estimate the mean RUL of a continuously degrading system under dynamic operational conditions and subjected to condition monitoring at short equi-distant intervals. The dynamic nature of the operational conditions is described by a discrete-time Markov chain, and their influences on the degradation signal are quantified by degradation rates and signal jumps in the degradation model. The uniqueness of our proposed approach is formulating the RUL prediction problem in a semi-Markov decision process framework, by which the system mean RUL can be obtained through the solution to a limited number of equations. To extend the use of our proposed approach in real applications, different failure standards according to different operational conditions are also considered. The application and effectiveness of this approach are illustrated by a turbofan engine dataset and a comparison with existing results for the same dataset.

A Throughput-Aware Joint Vehicle Route and Access Network Selection Approach Based on SMDP

In intelligent transportation system(ITS), the interworking of vehicular networks(VN) and cellular networks(CN) is proposed to provide high-data-rate services to vehicles. As the network access quality for CN and VN is location related, mobile data offloading(MDO), which dynamically selects access networks for vehicles, should be considered with vehicle route planning to further improve the wireless data throughput of individual vehicles and to enhance the performance of the entire ITS. In this paper, we investigate joint MDO and route selection for an individual vehicle in a metropolitan scenario. We aim to improve the throughput of the target vehicle while guaranteeing its transportation efficiency requirements in terms of traveling time and distance. To achieve this objective, we first formulate the joint route and access network selection problem as a semi-Markov decision process(SMDP). Then we propose an optimal algorithm to calculate its optimal policy. To further reduce the computation complexity, we derive a suboptimal algorithm which reduces the action space. Simulation results demonstrate that the proposed optimal algorithm significantly outperforms the existing work in total throughput and the late arrival ratio.Moreover, the heuristic algorithm is able to substantially reduce the computation time with only slight performance degradation.

A minimization problem of the risk probability in first passage semi-Markov decision processes with loss rates

This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.

First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs

This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal （or ε-optimal） stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.

Survivability modeling and analysis on 3D mobile ad-hoc networks

Most existing work on survivability in mobile ad-hoc networks(MANETs) focuses on two dimensional(2D) networks.However,many real applications run in three dimensional(3D) networks,e.g.,climate and ocean monitoring,and air defense systems.The impact on network survivability due to node behaviors was presented,and a quantitative analysis method on survivability was developed in 3D MANETs by modeling node behaviors and analyzing 3D network connectivity.Node behaviors were modeled by using a semi-Markov process.The node minimum degree of 3D MANETs was discussed.An effective approach to derive the survivability of k-connected networks was proposed through analyzing the connectivity of 3D MANETs caused by node misbehaviors,based on the model of node isolation.The quantitative analysis of node misbehaviors on the survivability in 3D MANETs is obtained through mathematical description,and the effectiveness and rationality of the proposed approach are verified through numerical analysis.The analytical results show that the effect from black and gray attack on network survivability is much severer than other misbehaviors.

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

The reliability of power transformers is subject to service age and health condition.This paper proposes a practical model for the evaluation of two reliability indices:survival function(SF)and mean residual life(MRL).In the proposed model,the periodical modeling of power transformers are considered for collecting the information on health conditions.The corresponding health condition is assumed to follow a continuous semi-Markov process for representing a state transition.The proportional hazard model(PHM)is introduced to incorporate service age and health condition into hazard rate.In addition,the proposed model derives the analytical formulas for and offers the analytical evaluation of SF and MRL.SF and MRL are calculated for new components and old components,respectively.In both cases,the proposed model offers rational results which are compared with those obtained from comparative models.The results obtained by the contrast of the proposed analytical method and the Monte Carlo method.The impact of differentmodel parameters and the coefficient of variation(CV)on reliability indices are discussed in the case studies.

Optimization of dynamic sequential test strategy for equipment health management

Testing is the premise and foundation of realizing equipment health management （EHM）. To address the problem that the static periodic test strategy may cause deficient test or excessive test, a dynamic sequential test strategy （DSTS） for EHM is presented. Considering the situation that equipment health state is not completely observable in reality, a DSTS optimization method based on partially observable semi-Markov decision pro- cess （POSMDP） is proposed. Firstly, an equipment health state degradation model is constructed by Markov process, and the control limit maintenance policy is also introduced. Secondly, POSMDP is formulated in great detail. And then, POSMDP is converted to completely observable belief semi-Markov decision process （BSMDP） through belief state. The optimal equation and the corresponding optimal DSTS, which minimize the long-run ex- pected average cost per unit time, are obtained with BSMDP. The results of application in complex equipment show that the proposed DSTS is feasible and effective.

The One-Dimensional Distribution and Construction of Semi-Markov Processes

In this paper, we obtain the transition probability of jump chain of semi-Markov pro- cess, the distribution of sojourn time and one-dimensional distribution of semi-Markov process. Furthermore, the semi-Markov process X（t, ω） is constructed from the semi-Markov matrix and it is proved that two definitions of semi-Markov process are equivalent.

Backscattering by sea of centimeter and millimeter waves at small grazing angle

Using experimental data reflected by the sea on specific radar cross-section （SRCS） at millimeter and centimeter waves, the approximations of the wind speed, angle of the sea surface radiation and polarization of the incident field can be calculated. The simulation model of the scattered signal has been proposed on the basis of the semi-Markov nested processes. For the first time it has been proved that for the description of reflections at spikes and pauses, it is possible to use finite atomic functions. The proposed model allows us to estimate the baekscatter intensity of millimeter and centimeter radio waves by the sea at grazing angle of surface radiation, as well as to simulate scattered signal.

THE BOREL STATE SPACE SEMI-MARKOVDECISION PROCESS WITH EXPECTED TOTAL REWARDS IN A SEMI-MARKOV ENVIRONMENT

This paper investigates the Borel state space semi-Markov decision process (SMDP) with the criterion of expected total rewards in a semi-Markov environment. It describes a system which behaves like a SMDP except that the system is influenced by its environment modeled by a semi-Markov process. We transform the SMDP in a semiMarkov environment into an equivalent discrete time Markov decision process under the condition that rewards are all positive or all negative, and obtain the optimality equation and some properties for it.

Optimal stopping time on discounted semi-Markov processes

This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.

Probabilistic Approach to Risk Analysis of Chemical Spills at Sea

Risk analysis of chemical spills at sea and their consequences for sea environment are discussed. Mutual interactions between the process of the sea accident initiating events, the process of the sea environment threats, and the process of the sea environment degradation are investigated. To describe these three particular processes, the separate semi-Markov models are built. Furthermore, these models are jointed into one general model of these processes interactions. Moreover, some comments on the method for statistical identification of the considered models are proposed.