Integral stochastic optimal design criteria in linear models

Within the framework of classical linear regression model integral optimal design criteria of stochastic nature are considered and their properties are established. Their limit behaviour generalizes that of the distance stochastic optimality criterion. As an example a line fit model is taken. Acknowledgement. I would like to thank the referees for their constructive comments which improved the paper.     

Optimal Dividend Payment Strategy under Stochastic Interest Force

This paper attempts to study the optimal dividend barrier strategy in risk analysis of an insurance company under stochastic discount interest. Based on stochastic perturbation methodology, we first describe the random of interest by Wiener Process and Poisson process and yield some theoretical results satisfied by optimal dividend barrier. In the case of an exponential individual claim distribution, a group of barrier values are obtained. Meanwhile we also discuss the effect of stochastic interest on the barrier by data analysis and direct interpretations about interest models. It is found that the barrier is more sensitive to constant interest force than other parameters in interest model and the effect of diffusion coefficient on barrier is less sensitive than that of Poisson coefficient. These all provide insights into the effect of stochastic interest on the optimal barrier, and show the importance of introducing stochastic interest. Finally, we propose several meaningful and follow-up problems, for example, changing the criterion of finding the optimal barrier and discussing under more extended risk models.     

局部平稳性未知条件下STAR模型的线性性检验

本文讨论了局部随机游走STAR模型、局部随机趋势STAR模型的线性性检验问题,构造了Wald类检验统计量,推导出了这些统计量的极限分布,并分析了这些统计量有限样本下的统计特性;本文提出了在局部平稳性未知的条件下,进行STAR模型的线性性检验方法,构建了稳健的检验统计量。检验功效与检验水平分析表明,该统计量具有良好的检验水平及较高的检验功效。     

工程抗灾设防标准的优化

合理确定抗灾设防标准是抗灾工程设计中的关键问题。本文结合抗灾工程的失效特点，提出了模糊失效准则，并对灾害破坏等级进行模糊划分；同时，针对灾害发生的随机性，分析了任一设防标准下可能出现的损失情况，定义了过设损失，并提出最优设防标准化的目标函数中应同时考虑失效损失和过设损失。     

Stochastic optimization model for distribution and evacuation planning (A case study of Tehran earthquake)

In this study, a stochastic multi-objective mixed-integer mathematical programming is proposed for logistic distribution and evacuation planning during an earthquake. Decisions about the pre- and post-phases of the disaster are considered seamless. The decisions of the pre-disaster phase relate to the location of permanent relief distribution centers and the number of the commodities to be stored. The decisions of the second phase are to determine the optimal location for the establishment of temporary care centers to increase the speed of treating the injured people and the distribution of the commodities at the affected areas. Humanitarian and cost issues are considered in the proposed models through three objective functions. Several sets of constraints are also considered in the proposed model to make it flexible to handle real issues. Demands for food, blood, water, blanket, and tent are assumed to be probabilistic which are related to several complicated factors and modeled using a complicated network in this study. A simulation is setup to generate the probabilistic distribution of demands through several scenarios. The stochastic demands are assumed as inputs for the proposed stochastic multi-objective mixed integer mathematical programming model.The model is transformed to its deterministic equivalent using chance constraint programming approach. The equivalent deterministic model is solved using an efficient epsilon-constraint approach and an evolutionary algorithm, called non-dominated sorting genetic algorithm (NSGA-II). First several illustrative numerical examples are solved using both solution procedures. The performance of solution procedures is compared and the most efficient solution procedure, i.e., NSGA-II, is used to handle the case study of Tehran earthquake. The results are promising and show that the proposed model and the solution approach can handle the real case study in an efficient way.     

On DS-optimal Design Matrices with Restrictions on Rows or Columns

The distance stochastic optimality criterion is considered in a linear regression setting with two possible experimental regions. The first region consists of design matrices with restrictions on their rows, while the second consists of design matrices with restrictions on their columns.     

完全信息下的最优保费控制问题研究

应用最大值原理研究了一类完全信息下最优保费控制问题,考虑了折现因子为函数且具有终端条件限制的情况,建立了完全信息下的正倒向随机控制系统。获得了唯一的递归的最优保费策略。     

Optimal static customer routing in a closed queuing network

In this paper we analyse the routing of customers in a general closed queuing network which satisfies a product-form assumption. We prove that there are optimal deterministic routing rules, and we provide an algorithm to compute a Nash equilibrium point of the stochastic game in which the players are the customers. Constrained optimal routing rules are also considered.     

DS-optimal designs in one way ANOVA

Characterization and construction of optimal designs using the familiar optimality criteria, for example A-, D- and E-optimality are well studied in the literature. However the study of the Distance Optimality (DS-) criterion introduced by Sinha (1970) has very recently drawn attention of researchers. In the present article, we consider the singularly estimable full rank problem of estimating the full set of elementary treatment contrasts using the DS optimality criterion in the set up of a one way ANOVA model. Using a limit argument it turns out that a CRD in which difference between any two allocation numbers is at the most unity is uniquely DS-optimal. Acknowledgement. We are thankful to Prof. B. K. Sinha for suggesting the problem to us and many helpful discussions with him. We are also thankful to the referees for drawing our attention to the reference of Bischoff (1995) and many helpful comments.     

Analysis of optimal dynamic withdrawal policies in withdrawal guarantee products

Guaranteed Minimum Withdrawal Benefits (GMWB) are popular riders in variable annuities with withdrawal guarantees. With withdrawals spread over the life of the annuities contract, the benefit promises to return the entire initial annuitization amount irrespective of the market performance of the underlying fund portfolio. Treating the dynamic withdrawal rate as the control variable, the earlier works on GMWB have considered the construction of a continuous singular stochastic control model and the numerical solution of the resulting pricing model. This paper presents a more detailed characterization of the pricing properties of the GMWB and performs a full mathematical analysis of the optimal dynamic withdrawal policies under the competing factors of time value of fund, optionality value provided by the guarantee and penalty charge on excessive withdrawal. When a proportional penalty charge is applied on any withdrawal amount, we can reduce the pricing formulation to an optimal stopping problem with lower and upper obstacles. We then derive the integral equations for the determination of a pair of optimal withdrawal boundaries. When a proportional penalty charge is applied on the amount that is above the contractual withdrawal rate, we manage to characterize the behavior of the optimal withdrawal boundaries that separate the domain of the pricing models into three regions: no withdrawal, continuous withdrawal at the contractual rate and an immediate withdrawal of a finite amount. Under certain limiting scenarios such as a high policy fund value, the time close to expiry, or a low value of guarantee account, we manage to obtain analytical approximate solution to the singular stochastic control model of dynamic withdrawals.     

A stochastic characterization of Loewner optimality design criterion in linear models

In this paper we present a new stochastic characterization of the Loewner optimality design criterion. The result is obtained by proving a generalization to the well known corollary of Anderson's theorem. Certain connections between the Loewner optimality and the stochastic distance optimality design criterion are showed. We also present applications and generalizations of the main result. Received: 9 August 2000     

An algorithm for the solution of stochastic optimal control problems for large nonlinear econometric models

This paper considers the problem of solving an optimal control problem for large dynamic economic models which are both nonlinear and stochastic. It proposes a technique which combines conventional deterministic optimal control algorithms with the procedure of stochastic simulation, which calculates a numerical approximation to the distribution of the models endogenous variables. The new technique is computationally feasible for even large nonlinear models and, as an illustration of this, the Bank of England's large quarterly forecasting model is used in an example.     

Precautionary behavior and consumer information: A Markov process approach

This paper explores the role of consumer confidence in the equilibrium of a dynamic macroeconomic growth model with rational expectations. Consumers face an uncertain future income stream due to a Markov stochastic process that affects production. Changes in the properties of this process change consumer information sets and optimal policies in the rational expectations format. Increases in “persistence” in the shock process are considered; this is identified with the consumer's subjective assessment of future economic conditions. Two cases are considered: where either good or bad states of the process are more likely to persist into the future, and where bad states persist unconditionally at the expense of good. Consistent with earlier treatments of savings under uncertainty (Barsky, Mankiw and Zeldes 1986, and Skinner 1988), the consumer's response to increased income uncertainty is to exhibit precautionary saving behavior. The infinite-horizon growth model format used offers significant improvement over other finite-horizon life cycle models. Specifically, the model is a full general equilibrium model and the solutions are rational expectations solutions. The technique also is easily adapted to other recursive decision problems under uncertainty.     

Responsibility accounting and asymmetry of information

This paper uses the principal-agent model to show that a manager's optimal compensation should generally include non-controllable factors of production such as the firm's investment in capital. This implies that the managerial accounting distinction between profit and investment centres is artificial. Examples are shown in which the ROI or RI criteria could be optimal for compensating managers implying that the optimal compensation criterion is very much specific to the firm's production and risk parameters. Thus, the debate about which criterion is more appropriate is vacuous.     

Planning in an uncertain environment: Stochastic goal programming using the versatility criterion

This article presents a planning model that applies the versatility criterion to goal programming problems with uncertainty about the constraints which define the set of feasible decisions. Some of the constraint parameters are assumed to be stochastic variables with a joint normal distribution. The solution sought maximizes the probability of satisfying all the constraints. A nonlinear programming model is set out which can be solved by using numerical integration at every step. An illustrative example is provided which shows the possible application of the versatility model to land-use planning.     

双运量约束下的OD分布与随机用户均衡交通分配组合模型

建立了在起点交通产生总量固定和在讫点交通吸引总量固定约束下的OD分布与随机用户均衡交通分配模型，并证明了该极值模型与随机用户均衡及OD分布要求的等价性，并设计了启发式算法来求解。     

A dynamic equilibrium model of search, production, and exchange

We study a general equilibrium model where agents search for production and trading opportunities, that generalizes the existing literature by considering a large number of differentiated commodities and agents with idiosyncratic tastes. Thus, agents must choose nontrivial exchange as well as production strategies. We consider decreasing, constant, and increasing returns to scale in the matching technology, and characterize the circumstances under which there exist multiple steady state equilibria, or multiple dynamic equilibria for given initial conditions. We also characterize the existence of dynamic equilibria that are limit cycles. Equilibria are not generally optimal, and when multiple equilibria coexist they may be ranked. We analyze comparative statics and find that certain intuitive results do not necessarily hold without restrictions on the stochastic structure.     

Forecasting exchange rates using feedforward and recurrent neural networks

In this paper we investigate the out-of-sample forecasting ability of feedforward and recurrent neural networks based on empirical foreign exchange rate data. A two-step procedure is proposed to construct suitable networks, in which networks are selected based on the predictive stochastic complexity (PSC) criterion, and the selected networks are estimated using both recursive Newton algorithms and the method of nonlinear least squares. Our results show that PSC is a sensible criterion for selecting networks and for certain exchange rate series, some selected network models have significant market timing ability and/or significantly lower out-of-sample mean squared prediction error relative to the random walk model.     

Bayesian model averaging for mortality forecasting using leave-future-out validation

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to some well-documented drawbacks, including model misspecification, parameter uncertainty, and overfitting. To address these issues we first consider mortality modeling in a Bayesian negative-binomial framework to account for overdispersion and the uncertainty about the parameter estimates in a natural and coherent way. Model averaging techniques are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation and compare them to standard Bayesian model averaging (BMA) based on marginal likelihood. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets, along with a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on an out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.     

集装箱空箱调运优化问题的研究

在分析集装箱空箱流转过程的基础上,提出建立基于海陆运整体成本最优的集装箱空箱调运随机性优化模型,并将粒子群算法与随机模拟技术相结合用于求解机会约束规划。最后通过对测试算例进行求解,验证了该模型和算法的合理性和有效性。