A quantile-based approach to system selection

We propose a quantile-based ranking and selection (R&S) procedure for comparing a finite set of stochastic systems via simulation. Our R&S procedure uses a quantile set of the simulated probability distribution of a performance characteristic of interest that best represents the most appropriate selection criterion as the basis for comparison. Since this quantile set may represent either the downside risk, upside risk, or central tendency of the performance characteristic, the proposed approach is more flexible than the traditional mean-based approach to R&S. We first present a procedure that selects the best system from among K systems, and then we modified that procedure for the case where K − 1 systems are compared against a standard system. We present a set of experiments to highlight the flexibility of the proposed procedures.     

Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR

Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. In this paper, we will establish some logical connections among VaRs, conditional-VaR, stochastic dominance, and utility maximization. Though supported to some extents with unanimous choices by some specific groups of expected or non-expected-utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable – they can only provide partial and incomplete risk assessments for risky prospects.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

一种航空客机选型的随机多属性决策方法

为解决航空公司客机选型决策中,需要使用的旅客需求信息为随机信息的问题,本文研究了考虑随机信息的航空客机选型多属性决策方法.首先在分析飞机选型工作流程的基础上,建立了航空客机选型评价指标体系;然后针对指标信息中既有数值信息又有随机信息的特点,给出了一种航空客机选型的随机多属性决策方法;最后通过一个算例说明了本文给出方法的可行性和有效性.相关原理和方法可以扩展应用到新能源汽车服务网络方案选择、移动信息服务开发项目选择等决策问题.     

Portfolio construction based on stochastic dominance and target return distributions

Mean-risk models have been widely used in portfolio optimization. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective functions. A model is proposed in which the aspiration points relate to ordered outcomes for the portfolio return. This concept is extended by additionally specifying reservation points, which act pre-emptively in the optimization model. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated.     

二阶随机占优约束下考虑偏度的投资组合模型

在DentchevaRuszczynski(2006)模型的基础上,考虑偏度对构建投资组合的影响,建立了二阶随机占优约束下最大化组合收益率偏度的投资组合优化模型,并应用分段线性近似方法将模型转化为一个非线性混合整数规划问题.利用中国股票市场的历史数据对所建模型进行了实证分析,结果表明,所建新模型比均值-方差-偏度模型和市场指数具有更稳健的表现.     

Global attractors for a discrete selection model with periodic immigration

A one-island selection-migration model is used to study the periodic immigration of a population of fixed allele frequency into a natural population. Density-dependent selection and immigration are the primary factors affecting the demographic and genetic change in the island population. With the assumptions of complete dominance (CD) or no dominance (ND) and homozygote superiority in fitness, the existence and location of global attractors are established. Analysis of this model provides rudimentary information about the migration of transgenes into a natural population.     

Stochastic system for generalized polytropic filtration

In this paper, we study a certain class of stochastic quasilinear parabolic equations describing a generalized polytropic elastic filtration in the framework of variable exponents Lebesgue and Sobolev spaces. We establish an existence result in the infinite dimensional framework of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions, and the governing equations are subjected to cylindrical Wiener processes. We use a Galerkin method, derive crucial a priori estimates for the approximate solutions, and combine profound analytic and probabilistic compactness results in order to pass to the limit. Several difficulties arise in obtaining these uniform bounds and passing to the limit since the nonlinear elliptic part of the leading operator admits nonstandard growth. Apart from adapting the above essential tools, we extend classical methods of monotonicity to the present situation.     

多总体二阶随机占优对无约束的检验问题

该文将利用保序回归估计和Bootstrap方法对多总体二阶随机占优对无约束的检验问题进行研究,具体步骤如下:首先,利用保序回归估计和经验分布函数构造检验统计量;然后,利用Bootstrap方法给出检验问题的临界值和p值;最后,通过Monte Carlo模拟来说明该文所提出方法的可行性.     

Stochastic linear knapsack programming problem and its application to a portfolio selection problem

In this paper a probability maximization model of a stochastic linear knapsack problem is considered where the random variables consist of several groups with mutually correlated ones. We propose a solution algorithm to the equivalent nonlinear fractional programming problem with a simple ranking method. This approach will be effectively applied to one of the portfolio selection problems.     

Two-Stage Nested Partitions Method for Stochastic Optimization

We address the problem of optimizing over a large but finite set when the objective function does not have an analytical expression and is evaluated using noisy estimation. Building on the recently proposed nested partitions method for stochastic optimization, we develop a new approach that combines this random search method and statistical selection for guiding the search. We prove asymptotic convergence and analyze the finite time behavior of the new approach. We also report extensive numerical results to illustrate the benefits of the new approach.     

Stochastic models for first-order kinetics of biochemical oxygen demand with random initial conditions, inputs, and coefficients

Biochemical oxygen demand (BOD) is a parameter of prime importance in surface water pollution studies and in the design and operation of waste-water treatment plants. A general, stochastic analytical model (denoted S1) is developed for the temporal expectation and (heteroscedastic) variance of first-order BOD kinetics. The model is obtained by integrating the moment equation, which is derived from the mathematical theory of stochastic differential equations. This model takes into account random initial conditions, random inputs, and random coefficients, which appear in the model formulation as initial condition (σ_O²), input (σ_l²), and coefficient (σ_c²) variance parameters, respectively. By constraining these three variance parameters to either vanish or to be nonnegative, model S1 is allowed (under appropriate combinations of the constraints) to split into six stochastic “submodels” (denoted S2 to S7), with each of these submodels being a particular case of the general model. Model S1 also degenerates to the deterministic model (denoted D) when each of the variance parameters vanish. The deterministic parameters (i.e., the rate coefficient and the ultimate BOD) and the stochastic variance parameters of the seven models are estimated on sets of replicated BOD data using the maximum likelihood principle. In this study, two (S5 and S7) of these seven stochastic models are found to be appropriate for BOD. The stochastic input (S5) model (i.e., null initial condition and coefficient variance parameters) shows the best prediction capabilities, while the next best is the stochastic initial condition (S7) model (i.e., null input and coefficient variance parameters).     

Scenario-based portfolio selection of investment projects with incomplete probability and utility information

In the selection of investment projects, it is important to account for exogenous uncertainties (such as macroeconomic developments) which may impact the performance of projects. These uncertainties can be addressed by examining how the projects perform across several scenarios; but it may be difficult to assign well-founded probabilities to such scenarios, or to characterize the decision makers’ risk preferences through a uniquely defined utility function. Motivated by these considerations, we develop a portfolio selection framework which (i) uses set inclusion to capture incomplete information about scenario probabilities and utility functions, (ii) identifies all the non-dominated project portfolios in view of this information, and (iii) offers decision support for rejection and selection of projects. The proposed framework enables interactive decision support processes where the implications of additional probability and utility information or further risk constraints are shown in terms of corresponding decision recommendations.     

Stochastic comparison algorithm for continuous optimization with estimation

The problem of stochastic optimization for arbitrary objective functions presents a dual challenge. First, one needs to repeatedly estimate the objective function; when no closed-form expression is available, this is only possible through simulation. Second, one has to face the possibility of determining local, rather than global, optima. In this paper, we show how the stochastic comparison approach recently proposed in Ref. 1 for discrete optimization can be used in continuous optimization. We prove that the continuous stochastic comparison algorithm converges to an -neighborhood of the global optimum for any >0. Several applications of this approach to problems with different features are provided and compared to simulated annealing and gradient descent algorithms.This work was supported in part by the National Science Foundation under Grants EID-92-12122 and ECS-88-01912, and by a Grant from United Technologies/Otis Elevator Company.     

Stochastic dominance and mean–variance measures of profit and loss for business planning and investment

In this paper, we first extend the stochastic dominance (SD) theory by introducing the first three orders of both ascending SD (ASD) and descending SD (DSD) to decisions in business planning and investment to risk-averse and risk-loving decision makers so that they can compare both return and loss. We provide investors with more tools for empirical analysis, with which they can identify the first-order ASD and DSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors and business planners to identify the third order ASD and DSD prospects and make better choices.     

On the Boundedness of Asymptotic Stability Regions for the Stochastic Theta Method

The stochastic theta method gives a computational procedure for simulating ordinary stochastic differential equations. The method involves a free parameter, . Here, we characterise the precise value of beyond which the region of linear asymptotic stability of the method becomes unbounded. The cutoff point is seen to differ from that in the deterministic case. Computations that suggest further results are also given.     

Stochastic bounds for a polling system

In this note we consider two queueing systems: a symmetric polling system with gated service at allN queues and with switchover times, and a single-server single-queue model with one arrival stream of ordinary customers andN additional permanently present customers. It is assumed that the combined arrival process at the queues of the polling system coincides with the arrival process of the ordinary customers in the single-queue model, and that the service time and switchover time distributions of the polling model coincide with the service time distributions of the ordinary and permanent customers, respectively, in the single-queue model. A complete equivalence between both models is accomplished by the following queue insertion of arriving customers. In the single-queue model, an arriving ordinary customer occupies with probabilityp _i a position at the end of the queue section behind theith permanent customer,i = l, ...,N. In the cyclic polling model, an arriving customer with probabilityp _i joins the end of theith queue to be visited by the server, measured from its present position.For the single-queue model we prove that, if two queue insertion distributions {p _{i, i} = l, ...,N} and {q _{i, i} = l, ...,N} are stochastically ordered, then also the workload and queue length distributions in the corresponding two single-queue versions are stochastically ordered. This immediately leads to equivalent stochastic orderings in polling models.Finally, the single-queue model with Poisson arrivals andp ₁ = 1 is studied in detail.Part of the research of the first author has been supported by the Esprit BRA project QMIPS.     

二阶随机控制变点的Kolmogrov型检验和估计

基于Kolmogrov型统计量和Kiefer过程,对一样本情形,我们讨论了二阶随机控制变点的检验和估计到了检验统计量的渐近分布且用模拟方法给出了其有限样本的分位数,并证明了变点的估计为强相合的。     

Controlled multistage selection procedures for comparison with a standard

Comparison with a standard is a general multiple comparison problem, where each system is required to be compared to a single system, referred to as a “standard”, as well as to other alternative systems. The goal is to determine the best system among a number of systems that are better than the standard, or to select the standard when it is equal to or better than the other alternatives. Kim (2005) proposed an efficient fully sequential procedure for comparison with a standard, that obtains a single observation at each stage from the surviving systems, and is one of the most efficient existing procedures. We develop two provably valid multistage selection procedures that take a number of observations from each system and update the variance estimators at each stage. We also employ appropriate control variate technique for each procedure to further improve the efficiency. Empirical results are provided to demonstrate that the proposed procedures are statistically and computationally more efficient than existing fully sequential procedures.     

An integrated FCM and fuzzy soft set for supplier selection problem based on risk evaluation

Supplier selection problem, considered as a multi-criteria decision-making (MCDM) problem, is one of the most important issues for firms. Lots of literatures about it have been emitted since 1960s. However, research on supplier selection under operational risks is limited. What’s more, the criteria used by most of them are independent, which usually does not correspond with the real world. Although the analytic network process (ANP) has been proposed to deal with the problems above, several problems make the method impractical. This study first integrates the fuzzy cognitive map (FCM) and fuzzy soft set model for solving the supplier selection problem. This method not only considers the dependent and feedback effect among criteria, but also considers the uncertainties on decision making process. Finally, a case study of supplier selection considering risk factors is given to demonstrate the proposed method’s effectiveness.