An SDP approach for multiperiod mixed 0–1 linear programming models with stochastic dominance constraints for risk management

In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage case and includes both the first-order and second-order constraints. We propose a stochastic dynamic programming (SDP) solution approach, where one has to overcome the negative impact of the cross-scenario constraints on the decomposability of the model. In our computational experience we compare our SDP approach against a commercial optimization package, in terms of solution accuracy and elapsed time. We use supply chain planning instances, where procurement, production, inventory, and distribution decisions need to be made under demand uncertainty. We confirm the hardness of the testbed, where the benchmark cannot find a feasible solution for half of the test instances while we always find one, and show the appealing tradeoff of SDP, in terms of solution accuracy and elapsed time, when solving medium-to-large instances.     

基于信息间隙决策理论的发电商电量分配策略

在电力市场环境下,发电商需要在现货市场、双边合同和期权等交易选择中合理分配交易电量.针对现货市场电价的严重不确定性,采用信息间隙决策理论,提出风险回避发电商在多种交易选择中的电量分配鲁棒决策模型.算例仿真验证了模型方法的合理性和有效性,并表明,所提出方法提供了发电商不同预期收益目标下的电量分配策略可抵抗的现货价格波动幅度,风险回避发电商可由此评价不同的电量分配策略,并采用相应的策略来保证预期收益目标.     

Two-stage stochastic programming supply chain model for biodiesel production via wastewater treatment

This paper presents a two-stage stochastic programming model used to design and manage biodiesel supply chains. This is a mixed-integer linear program and an extension of the classical two-stage stochastic location-transportation model. The proposed model optimizes not only costs but also emissions in the supply chain. The model captures the impact of biomass supply and technology uncertainty on supply chain-related decisions; the tradeoffs that exist between location and transportation decisions; and the tradeoffs between costs and emissions in the supply chain. The objective function and model constraints reflect the impact of different carbon regulatory policies, such as carbon cap, carbon tax, carbon cap-and-trade, and carbon offset mechanisms on supply chain decisions. We solve this problem using algorithms that combine Lagrangian relaxation and L-shaped solution methods, and we develop a case study using data from the state of Mississippi. The results from the computational analysis point to important observations about the impacts of carbon regulatory mechanisms as well as the uncertainties on the performance of biocrude supply chains.     

Tax impact on multi-stage mean-variance portfolio allocation

We investigate the sensitivity to tax change of multi‐stage portfolio allocation over a discrete time investment horizon. Special taxation rules within wrappers grouped a number of risky assets are integrated with multi‐stage linear or quadratic stochastic programming in the mean‐variance framework. The uncertainty on the returns of assets is specified as a scenario tree generated by a simulation‐based approach. We adjust different values on capital gains tax under different asset bounds and risk levels. The tax impact in the yearly reallocation of the investments for a typical case with an annual fixed withdrawal that utilizes completely the option of taper relief is also explored. Our computational results show that taxes, combined with other effects such as risk and investment upper bounds, have a significant performance impact on portfolio allocation as well as diversification over wrappers. Yet, investment strategies can be made robust to changes in taxation.     

An agent-based stochastic ruler approach for a stochastic knapsack problem with sequential competition

We examine a situation in which a decision-maker executes a sequence of resource allocation decisions over time, but the availability of the indivisible resources at future epochs is uncertain due to actions of competitors. We cast this problem as a specialized type of stochastic knapsack problem in which the uncertainty of item (resource) availability is induced by competitors concurrently filling their own respective knapsacks. Utilizing a multi-period bounded multiple-choice knapsack framework, we introduce a general discrete stochastic optimization model that allows a nonlinear objective function, cardinality constraints, and a knapsack capacity constraint. Utilizing a set of greedy selection rules and agent-based modeling to simulate the competitors’ actions, we solve the problem with a stochastic ruler approach that incorporates beam search to determine item selection of the types specified by the solution representation. We illustrate the computational effectiveness of our approach on instances motivated by a sports league draft as well as generic problem instances based on the knapsack literature.     

Stochastic robustness metric and its use for static resource allocations

This research investigates the problem of robust static resource allocation for distributed computing systems operating under imposed Quality of Service (QoS) constraints. Often, such systems are expected to function in a physical environment replete with uncertainty, which causes the amount of processing required to fluctuate substantially over time. Determining a resource allocation that accounts for this uncertainty in a way that can provide a probabilistic guarantee that a given level of QoS is achieved is an important research problem. The stochastic robustness metric proposed in this research is based on a mathematical model where the relationship between uncertainty in system parameters and its impact on system performance are described stochastically.The utility of the established metric is then exploited in the design of optimization techniques based on greedy and iterative approaches that address the problem of resource allocation in a large class of distributed systems operating on periodically updated data sets. The performance results are presented for a simulated environment that replicates a heterogeneous cluster-based radar data processing center. A mathematical performance lower bound is presented for comparison analysis of the heuristic results. The lower bound is derived based on a relaxation of the Integer Linear Programming formulation for a given resource allocation problem.     

Real-time optimization under parametric uncertainty: a probability constrained approach

Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.     

International portfolio optimisation with integrated currency overlay costs and constraints

International financial portfolios can be exposed to substantial risk from variations of the exchange rates between the countries in which they hold investments. Nonetheless, foreign exchange can both generate extra return as well as loss to a portfolio, hence rather than just being avoided, there are potential advantages to well-managed international portfolios. This paper introduces an optimisation model that manages currency exposure of a portfolio through a combination of foreign exchange forward contracts, thereby creating a “currency overlay” on top of asset allocation. Crucially, the hedging and transaction costs associated with holding forward contracts are taken into account in the portfolio risk and return calculations. This novel extension of previous overlay models improves the accuracy of the risk and return calculations of portfolios. Consequently, more accurate investment decisions are obtained through optimal asset allocation and hedging positions. Our experimental results show that inclusion of such costs significantly changes the optimal decisions. Furthermore, effects of constraints related to currency hedging are examined. It is shown that tighter constraints weaken the benefit of a currency overlay and that forward positions vary significantly across return targets. A larger currency overlay is advantageous at low and high return targets, whereas small overlay positions are observed at medium return targets. The resulting system can hence enhance intelligent expert decision support for financial managers.     

Determinants of IS sourcing decisions: A comparative study of transaction cost theory versus the resource-based view

Many organizations have employed the concepts of ‘asset specificity’ and ‘uncertainty’ from transaction cost theory (TCT), and ‘strategic resources’ from the resource-based view (RBV) as drivers of their information systems (ISs) sourcing decisions. They, however, face a dilemma when TCT and the RBV suggest different sourcing alternatives. The study identifies contexts where sourcing decisions made based on these two theories differ, and examines which theory accounts better for an organization's sourcing decisions. Results show that a high-specificity asset is a major driver of sourcing decisions. It overpowers the effects of uncertainty on sourcing decisions; while a non-strategic resource has no impact on sourcing decisions. In particular, where the two theories make conflicting predictions, organizations should not always outsource non-strategic resources. Non-strategic resources that involve high specificity should be retained internally. The paper concludes with implications for academics and practitioners, and a discussion of future research directions.     

Application of intelligent CAD paradigms to preliminary structural design

Structural design is the synthesis of structural systems and components in such a way that the system behaves as intended by the designer and meets the constraints imposed by physical laws and project requirements. The reasoning inherent in the design process is to be carried out on different levels and with different degrees of abstraction, uncertainty and impact on further design decisions. The nature of design operations ranges from schematic decisions based on heuristic considerations concerning system types and topology to parameter definitions concerning member material and geometry inferred from numerical computations. In our approach we explicitly distinguish between strategy and related expectations, design actions on a tactical level and local design modifications due to untypical conditions. Artificial intelligence techniques are applied such as planning methods, heuristic search and constraint programming which are used in a distinct manner on the different levels. The approach is discussed by examples taken from a prototype implementation for preliminary structural design.     

A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

A decision support system for strategic asset allocation

Strategic asset allocation is a crucial activity for any institutional or individual investor. Given a set of asset classes, the problem concerns the definition and management over time of the best asset mix to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. Although a considerable attention has been placed by the scientific community to address this problem by proposing sophisticated optimization models, limited effort has been devoted to the design of integrated framework that can be systematically used by financial operators. The paper presents a decision support system which integrates simulation techniques for forecasting future uncertain market conditions and sophisticated optimization models based on the stochastic programming paradigm. The system has been designed to be accessed via web and takes advantages of the increased computational power offered by high performance computing platforms. Real-world instances have been used to assess the performance of the decision support system also in comparison with more traditional portfolio optimization strategies.     

Distributing weights under hierarchical clustering: A way in reducing performance breakdown

This paper proposes a clustering asset allocation scheme which provides better risk-adjusted portfolio performance than those obtained from traditional asset allocation approaches such as the equal weight strategy and the Markowitz minimum variance allocation. The clustering criterion used, which involves maximization of the in-sample Sharpe ratio (SR), is different from traditional clustering criteria reported in the literature. Two evolutionary methods, namely Differential Evolution and Genetic Algorithm, are employed to search for such an optimal clustering structure given a cluster number. To explore the clustering impact on the SR, the in-sample and the out-of-sample SR distributions of the portfolios are studied using bootstrapped data as well as simulated paths from the single index market model. It was found that the SR distributions of the portfolios under the clustering asset allocation structure have higher mean values and skewness but approximately the same standard deviation and kurtosis than those in the non-clustered case. Genetic Algorithm is suggested as a more efficient approach than Differential Evolution for the purpose of solving the clustering problem.     

机构投资者的最优变现策略

相对于普通投资者,大规模持有某种资产的机构投资者在交易这种资产时,其行为会导致资产价格的单向变动,从而产生流动性风险。针对机构投资者在连续时间框架且股票价格服从几何布朗运动的情况,提出在随机冲击下其完全变现行为的最优变现策略,利用最优控制理论中的极小值原理研究其最优变现策略。敏感性分析表明,最优变现策略由市场价格波动率、资产的流动性和机构投资者的风险厌恶偏好共同决定。以深发展股票为例,验证了机构投资者在随机冲击下可根据上述结论选择合适的最优变现策略,降低其在市场中所面临的流动性风险,使得股票的账面价值更可能多的转换为实际收益。     

A capacitated hub location problem under hose demand uncertainty

In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem.     

Modification terms to the Black–Scholes model in a realistic hedging strategy with discrete temporal steps

ABSTRACT

Option pricing models generally require the assumption that stock prices are described by continuous-time stochastic processes. Although the time-continuous trading is easy to conceive theoretically, it is practically impossible to execute in real markets. One reason is because real markets are not perfectly liquid and purchase or sell any amount of an asset would change the asset price drastically. A realistic hedging strategy needs to consider trading that happens at discrete instants of time. This paper focuses on the impact and effect due to temporal discretization on the pricing partial differential equation (PDE) for European options. Two different aspects of temporal discretization are considered and used to derive the modification or correction source terms to the continuous pricing PDE. First the finite difference discretization of the standard Black–Scholes PDE and its modification due to discrete trading. Second the discrete trading leads to a discrete time re-balancing strategy that only cancels risks on average by using a discrete analogy of the stochastic process of the underlying asset. In both cases high order terms in the Taylor series expansion are used and the respective correction source terms are derived.     

Event tree based sampling

We develop a new sampling method, called an event tree-based sampling, which is suitable for the multistage stochastic programming formulation for the asset liability management. We find that our method captures a special structure inherited in the binomial lattice representation of an event tree, which is the essential part of the stochastic formulation of asset liability management under uncertainty.     

An adaptive modeling and asset allocation approach to financial markets based on discrete microstructure model

In previous works, it was verified that the discrete-time microstructure (DTMS) model, which is estimated by training dataset of a financial time series, may be effectively applied to asset allocation control on the following test data. However, if the length of test dataset is too long, prediction capability of the estimated DTMS model may gradually decline due to behavior change of financial market, so that the asset allocation result may become worse on the latter part of test data. To overcome the drawback, this paper presents a semi-on-line adaptive modeling and trading approach to financial time series based on the DTMS model and using a receding horizon optimization procedure. First, a long-interval identification window is selected, and the dataset on the identification window is used to estimate a DTMS model, which will be used to do asset allocation on the following short-term trading interval that is referred to as the trading window. After asset allocation is over on the trading window, the length-fixed identification window is then moved to a new window that includes the previous trading window, and a new DTMS model is estimated by using the dataset on the new identification window. Next, asset allocation continues on the next trading window that follows the previous trading window, and then the modeling and asset allocation process will go on according to the above steps. In order to enhance the flexibility and adaptability of the DTMS model, a comprehensive parameter optimization method is proposed, which incorporates particle swarm optimization (PSO) with Kalman filter and maximum likelihood method for estimating the states and parameters of DTMS model. Based on the adaptive DTMS model estimated on each identification window, an adaptive asset allocation control strategy is designed to achieve optimal control of financial assets. The parameters of the asset allocation controller are optimized by the PSO algorithm on each identification window. Case studies on Hang Seng Index (HSI) of Hong Kong stock exchange and S&P 500 index show that the proposed adaptive modeling and trading strategy can obtain much better asset allocation control performance compared with the parameters-fixed DTMS model.     

Probabilistic sensitivity analysis methods for general decision models

Probabilistic sensitivity analysis has previously been described for the special case of dichotomous decision trees. We now generalize these techniques for a wider range of decision problems. These methods of sensitivity analysis allow the analyst to evaluate the impact of the multivariate uncertainty in the data used in the decision model and to gain insight into the probabilistic contribution of each of the variables to the decision outcome. The techniques are illustrated using Monte Carlo simulation on a trichotomous decision tree. Application of these powerful tools permits the decision analyst to investigate the structure and limitations of more complex decision problems with inherent uncertainties in the data upon which the decisions are based. Probabilistic sensitivity measures can provide guidance into the allocation of resources to resolve uncertainty about critical components of medical decisions.