Short-term electricity procurement: A rolling horizon stochastic programming approach

This paper addresses the problem faced by a large electricity consumer in determining the optimal procurement plan over a short-term time horizon. The inherent complexity of the problem, due to its dynamic and stochastic nature, is dealt by means of the stochastic programming modeling framework. In particular, a two-stage problem is formulated with the aim of establishing the optimal amount of electricity to be purchased through bilateral contracts and in the Day-Ahead Electricity Market. Recourse actions are used to hedge against uncertainty related to future electricity prices and consumer’s needs. The optimal plan is defined so to minimize the overall cost and to control risk, which is measured in the form of violation of budget constraints. The stochastic model is dynamically solved in a rolling horizon fashion by iteratively considering more and more recent information and a planning horizon of decreasing length. Extensive numerical experiments have been carried out to assess the performance of the proposed dynamic decision approach. The results collected considering a real test case are very encouraging and provide evidence of the superiority of the approach also in comparison with other alternative procurement strategies.     

A multi-stage financial hedging approach for the procurement of manufacturing materials

This paper addresses the problem of mitigating procurement risk that arises from volatile commodity prices by proposing a hedging strategy within a multi-stage time frame. The proposed multi-stage hedging strategy requires a commodity futures position to be correctly initialised and rebalanced with adequate volumes of short/long positions, so as to reduce the volatility in the total procurement cost that would otherwise be generated by varying commodity spot prices. The novelty in the approach is the introduction of the rebalancing of commodity futures position at defined intermediate stages. To obtain an efficient or near optimal multi-stage hedging strategy, a discrete-time stochastic control model (DSCM) is developed. Numerical experiments and Monte Carlo simulation are used to show that the proposed multi-stage hedging strategy compares favourably with the minimal-variance hedge and the one-stage hedge. A close-form optimal solution is also presented for the case when procurement volume and price are independent.     

VaR测度下的风险对冲策略研究

本文分别在正态分布和任意分布设定下讨论最小在险价值(VaR)的风险对冲问题。在正态分布设定下,本文深入讨论最小方差对冲比率和最小VaR对冲比率的性质,并得出最小VaR对冲策略下组合收益率的均值和方差大于最小方差策略下组合收益率的均值和方差。在任意分布设定下,本文构建一种新的VaR对冲模型,该模型引入非参数核估计方法对VaR进行估计,然后基于VaR核估计量建立风险对冲问题,实现风险估计与风险对冲同步进行。实证结果非常稳健地表明,不做任何分布假设下的核估计法得到的风险对冲效果优于最小方差对冲策略和正态分布设定下的最小VaR对冲策略。     

The natural hedge of a gas-fired power plant

Electricity industries worldwide have been restructured in order to introduce competition. As a result, decision makers are exposed to volatile electricity prices, which are positively correlated with those of natural gas in markets with price-setting gas-fired power plants. Consequently, gas-fired plants are said to enjoy a “natural hedge.” We explore the properties of such a built-in hedge for a gas-fired power plant via a stochastic programming approach, which enables characterisation of uncertainty in both electricity and gas prices in deriving optimal hedging and generation decisions. The producer engages in financial hedging by signing forward contracts at the beginning of the month while anticipating uncertainty in spot prices. Using UK energy price data from 2006 to 2011 and daily aggregated dispatch decisions of a typical gas-fired power plant, we find that such a producer does, in fact, enjoy a natural hedge, i.e., it is better off facing uncertain spot prices rather than locking in its generation cost. However, the natural hedge is not a perfect hedge, i.e., even modest risk aversion makes it optimal to use gas forwards partially. Furthermore, greater operational flexibility enhances this natural hedge as generation decisions provide a countervailing response to uncertainty. Conversely, higher energy-conversion efficiency reduces the natural hedge by decreasing the importance of natural gas price volatility and, thus, its correlation with the electricity price.     

Inventory control under temporal demand heteroscedasticity

This paper studies an inventory control problem when the variance of demand is time-varying and exhibits temporal heteroscedasticity. We use a first-order autoregressive process to characterize the dynamic changes in the level of demand over time and a GARCH(1, 1) structure to describe the changes in the variance of demand. Under these demand settings, we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order-up-to-level policy. We show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance. The decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored. The relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated. Computational results show that ignoring temporal heteroscedasticity can increase firm’s inventory costs by as much as 30% when demand autocorrelation is highly positive.     

需求不确定下应急医疗服务站鲁棒配置模型与算法

大型突发事件发生后需要快速启动应急救灾网络,合理配置应急医疗服务站。本文考虑各应急医疗服务站选址节点需求的不确定性,引入三个不确定水平参数,构建四类不确定需求集合(box, ellipsoid, polyhedron和interval-polyhedron)对应的应急医疗服务站鲁棒配置模型,运用分支-切割算法求解,最后,进行需求扰动比例的灵敏度分析。算例结果表明,四类不确定需求集下的鲁棒配置模型中,ellipsoid不确定需求集合配置模型开放设施较少,总成本最小,鲁棒性较好。决策者还可以根据风险偏好选择不确定水平和需求扰动比例的组合,以使得总成本最小。     

Robust strategies for facility location under uncertainty

This paper considers a stochastic facility location problem in which multiple capacitated facilities serve customers with a single product, and a stockout probabilistic requirement is stated as a chance constraint. Customer demand is assumed to be uncertain and to follow either a normal or an ambiguous distribution. We study robust approximations to the problem in order to incorporate information about the random demand distribution in the best possible, computationally tractable way. We also discuss how a decision maker’s risk preferences can be incorporated in the problem through robust optimization. Finally, we present numerical experiments that illustrate the performance of the different robust formulations. Robust optimization strategies for facility location appear to have better worst-case performance than nonrobust strategies. They also outperform nonrobust strategies in terms of realized average total cost when the actual demand distributions have higher expected values than the expected values used as input to the optimization models.     

Multiple unit auctions with economies and diseconomies of scale

This paper discusses multiple unit auctions for industrial procurement where the cost structures of suppliers capture economies and diseconomies of scale caused by the nature of the production cost and the opportunity value of suppliers’ capacities. The problem of winner determination and demand allocation is proven to be NP-complete. We propose a binary tree algorithm with bounds (BTB) which efficiently exploits the model’s optimality properties. BTB outperforms general integer optimization software in computational time, especially with existence of substantial economies and diseconomies of scale. The algorithm complexity is linear in demand volume. This property allows for efficient handling of high volume auctions and thus leads to increased benefit for the overall system. Under the assumption of the myopic best response strategies, we investigate the behavior of suppliers and price dynamics for iterative (multiple round) bidding with appropriate allocation and stopping rules. The allocation rules, featured by several tie breakers for multiple optimal solutions to the allocation model in each round, are proposed to induce suppliers’ dominant strategies and to improve the system’s performance.     

Dynamic lot-sizing problem with demand time windows and container-based transportation cost

In this paper, we study the dynamic lot-sizing problem with demand time windows and container-based transportation cost. For each particular demand, there are corresponding earliest and latest times, and the duration between such earliest and latest times is the demand time window. If a demand is satisfied by a delivery within demand time window, then there is no holding or backlogging cost incurred. Our purpose is to satisfy demand at a minimum total cost, including setup cost, procurement cost, container cost, and inventory holding cost. This research is supported in part by Hong Kong RGC grant HKUST 6010/02E and NUS ARF grant R-266-000-019-112.     

Efficient and effective heuristics for the coordinated capacitated lot-size problem

Coordinating procurement decisions for a family of products that share a constrained resource, such as an ocean shipping container, is an important managerial problem. However due to the problem’s difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. This paper proposes two heuristics, for the capacitated, coordinated dynamic demand lot-size problem with deterministic but time-varying demand. In addition to inventory holding costs, the problem assumes a joint setup cost each time any member of the product family is replenished and an individual item setup cost for each item type replenished. The objective is to meet all customer demand without backorders at minimum total cost. We propose a six-phase heuristic (SPH) and a simulated annealing meta-heuristic (SAM). The SPH begins by assuming that each customer demand is met by a unique replenishment and then it seeks to iteratively maximize the net savings associated with order consolidation. Using SPH to find a starting solution, the SAM orchestrates escaping local solutions and exploring other areas of the solution state space that are randomly generated in an annealing search process. The results of extensive computational experiments document the effectiveness and efficiency of the heuristics. Over a wide range of problem parameter values, the SPH and SAM find solutions with an average optimality gap of 1.53% and 0.47% in an average time of 0.023 CPU seconds and 0.32 CPU seconds, respectively. The heuristics are strong candidates for application as stand alone solvers or as an upper bounding procedure within an optimization based algorithm. The procedures are currently being tested as a solver in the procurement software suite of a nationally recognized procurement software provider.     

The role of index bonds in universal currency hedging

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.     

Dynamic decision making for graphical models applied to oil exploration

We present a framework for sequential decision making in problems described by graphical models. The setting is given by dependent discrete random variables with associated costs or revenues. In our examples, the dependent variables are the potential outcomes (oil, gas or dry) when drilling a petroleum well. The goal is to develop an optimal selection strategy of wells that incorporates a chosen utility function within an approximated dynamic programming scheme. We propose and compare different approximations, from naive and myopic heuristics to more complex look-ahead schemes, and we discuss their computational properties. We apply these strategies to oil exploration over multiple prospects modeled by a directed acyclic graph, and to a reservoir drilling decision problem modeled by a Markov random field. The results show that the suggested strategies clearly improve the naive or myopic constructions used in petroleum industry today. This is useful for decision makers planning petroleum exploration policies.     

Analysis of hedge fund strategies using slack-based DEA models

Hedge funds have made a significant impact on the performance of world financial markets in recent times. Our objective in this paper is to develop a robust framework for the evaluation of hedge funds by incorporating a maximum number of performance measures through public data sources. We analyse the hedge fund strategies (styles) using a variety of classical risk-return measures with the help of slack-based Data Envelopment Analysis (DEA) models to determine a unique performance indicator. The main thrust is to investigate the risk return profile of 4730 hedge funds classified under 18 different strategies using multiple inputs and outputs. The originality of the work lies in applying Slack-Based DEA to decipher the risk-return profile of these strategies using advanced risk-return measures such as Value at Risk, drawdown, lower and higher partial moments and skewness. We find that the correlation between the ranking of hedge fund strategies based on Sharpe ratio and the DEA models is very low; at the same time, there is a significant correlation between rankings obtained by the application of DEA using different sets of input/output measures. We have also compared the DEA rankings with other traditional financial ratios such as modified Sharpe ratio, Sortino ratio and Calmar ratio. The paper also studies the impact of events such as the Asian financial crisis on the performance of hedge funds. The study around the event shows that only a relatively small number of strategies performed better during times of turmoil.     

Vendor managed inventory for environments with stochastic product usage

We develop technology to plan delivery routes for the supply of blood products to hospitals by a blood bank. The technology produces low cost, robust plans that hedge against the natural uncertainty associated with blood product usage at hospitals. The technology relies on sampling-based approaches involving integer programming and variable neighborhood search. An extensive computational study shows the efficacy of the two approaches and highlights the impact of product usage uncertainty on the resulting delivery plans.     

带有风能的智能电网多周期买电策略研究

本文研究带有风能随机供给的智能电网中传统能源的多周期买电问题,假设存在一个能源运营商集中负责智能电网传统能源的购买和消费。通过构建并求解动态规划模型,找到能源运营商在风能供给不确定性下的传统能源最优多周期买电策略。在最优买电策略下,能源运营商只有在当期电价足够小时才购买传统能源,其买电量与风能分布、价格信息和时间信息有关。在实际数据的基础之上,提供详实的数值实验对比研究了本文的最优买电策略和其他两种策略(实践中只考虑风能估计的策略和放弃利用风能的策略)在最小化总成本方面的效果,并验证了本文的最优买电策略在真实风能数据中的鲁棒性。     

Mean–Variance Optimal Adaptive Execution

Abstract

Electronic trading of equities and other securities makes heavy use of ‘arrival price’ algorithms that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean–variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies and that the improvement is larger for large initial positions.

We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with an arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are ‘aggressive-in-the-money’: they accelerate the execution when the price moves in the trader's favor, spending parts of the trading gains to reduce risk.     

Delta-hedging longevity risk under the M7–M5 model: The impact of cohort effect uncertainty and population basis risk

In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7–M5 model is developed and recommended as an industry standard for the assessment of population basis risk. In this paper, we contribute a delta hedging strategy for use with the M7–M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (2) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness.     

考虑突发事件状态转移的政府应急物资采购定价模型

突发事件发生后,应急物资需求量呈现爆发式增长,政府首先将常规物资调拨至受灾区,并根据阶段性救灾成果作出应急物资采购决策。突发事件状态总是不断发生转移,使得政府已采购的物资在状态好转时容易造成浪费,在状态持续恶化时又不足以满足突发需求,因此考虑突发事件状态转移情形的应急物资采购定价策略对提升政府应急物资保障能力尤为关键。为此,本研究引入数量柔性契约到政府与应急物资供应商组成的两级应急物资采购供应链,构建了基于突发事件状态转移的应急物资采购定价模型,推导得出政企达成合作的条件与双方最优决策策略,并对比分析了契约合作与分散非合作下的供应商利润与政府成本。进一步采用数值计算与敏感性分析验证该模型的有效性,讨论了若干外生变量对政企最优决策与双方成本收益的影响,提出重要的管理启示。研究表明,考虑突发事件状态转移的基于数量柔性契约的政府应急物资采购定价模型既可以有效提高应急物资储备水平,又能保障供应商的合理收益以及控制政府成本,实现了政企双赢。     

A Further Study of the Choice Between Two Hedging Strategies–the Continuous Case

In our previous work, the choice between two popular hedging strategies was studied under the assumption that the hedge position of the underlying portfolio follows a discrete-time Markov chain with boundary conditions. This paper aims to investigate the same problem for the continuous case. We first assume that the underlying hedge position follows an arbitrary continuous-time Markov process; we give the general formulas for long-run cost per unit time under two cost structures: (1) a fixed transaction cost (2) a non-fixed transaction cost. Then we consider the case where the underlying hedge position follows a Brownian motion with drift; we show that (i) re-balancing the hedge position to the initial position is always more cost-efficient than re-balancing it to the boundary for a fixed transaction cost; (ii) when the cost function satisfies certain conditions, re-balancing the hedge position to the initial position is more cost-efficient than re-balancing it to the boundary for a non-fixed transaction cost.     

组合投资β调整与效用最大化的套期比的选择

为了针对市场风险对风险资产的组合投资进行套期保值，一般认为要选择将组合投资多头和期货合同空头结合起来的头寸方差最小化的套期保值比率，也就是要选择使某一特定函数的期望效用最大化的套期保值比率。但是本认为，由于种种原因，人们更倾向于选择对简单风险最小头寸的套期保值比率。