价格随机条件下的应急双向期权数量弹性契约

旨在用期权应对批发价格波动的风险,用数量弹性契约来应对市场价格和市场需求随机波动带来的风险,探索双向期权数量弹性契约协调供应链的内在规律。将双向期权契约与数量弹性契约相融合,协调批发价、市场价格和市场需求均随机波动的供应链,寻找最优的供应链决策,并进行了算例仿真。研究结果表明：在批发价格波动时,采用双向期权弹性契约比采用基准数量弹性契约效果更好。双向期权弹性契约可以协调批发价格和市场价格均随机的供应链。     

随机需求条件下基于期权交易的供应链协调模型

〖HT5”H〗摘要： 〖HTSS〗期权契约作为一种供应链契约能使供应链达到协调。论文从基本的零售商订货模型出发,引入可交易的看涨期权,通过比较零售商的最优订货量和期权购买量,以及供应链整体的最优订货量和期权购买量,发现引入期权交易时,供应链达到最优订货时的利润总是大于零售商达到最优订货时的利润。并得出供应商可以通过调整期权契约参数来促使零售商主动将其最优订货量调节到协调时的供应链总体订货量水平的结论。     

Value of a put option to the risk-averse newsvendor

In this paper we consider an extension of the single-period inventory model with stochastic demand where a put option can be purchased to reduce losses resulting from low demand. The newsvendor not only chooses the order quantity but also determines the “strike price” and/or the “strike quantity” of the put option. As the buyer of the put option, the newsvendor pays the option writer an amount that equals the expected option payoff plus a risk premium and receives from the option writer the strike price (adjusted for salvage value) for each unit that the demand falls below the strike quantity. The newsvendor is risk-averse and attempts to maximize an expected utility function. We show that: (i) the same order quantity maximizes the expected profit with or without the option; and (ii) the strike price and strike quantity do not affect the newsvendor's maximum expected profit but they do affect the variance of the profit. We use concepts from stochastic dominance theory to prove the following result: if the newsvendor uses the expected profit maximizing order quantity and if she has a quadratic utility function, then maximizing her expected utility is equivalent to minimizing the variance of the profit. Sensitivity analysis results indicate that under poor economic conditions (low sale price/high purchase cost) it may not be optimal to purchase the option. We also find that when the option writer assumes a higher risk/return for the random option payoff (that he pays the newsvendor) the newsvendor can reduce her profit uncertainty by choosing the strike price or strike quantity optimally.     

Rewards-supply planning under option contracts in managing coalition loyalty programmes

We examine the problem of planning the supply of rewards in coalition loyalty programmes considering that the buyer–supplier relationships with commercial partners are governed by option contracts rather than wholesale price contracts similar to what is commonly used in practice. We develop a two-stage stochastic linear programme model with simple recourse which considers uncertain demand requirements, limited reward purchasing budgets, multiple programme partners of various sizes, point-liability control targets and overall profitability. A sampling average approximation scheme is used to solve the model. Numerical experiments show that option contracts perform better than wholesale price contracts when redemption demand uncertainty is high and the number of redemption partners is large. The results also suggest that the common practice of increasing redemption capacities is not the most effective way to cope with demand uncertainties. Programmes that reduce redemption demand variability and/or create better contracting structures are more promising in improving points-liability, redemption budget spending and overall profitability than traditional approaches.     

价格随机条件下看涨期权折扣契约的应急供应链协调研究

在突发事件造成市场需求与市场价格均随机波动的条件下,将期权与数量折扣契约融合,形成一种新的期权折扣契约,并用看涨期权折扣契约模型来协调供应链。通过海塞矩阵判断得知供应链存在最优决策,并进行算例分析。结果表明：当突发事件引起市场需求增加时,看涨期权折扣契约和数量折扣契约均能有效地提升供应链收益,且看涨期权折扣契约提升的幅度更大;当突发事件引起市场需求缩小时,2种契约均不能扭转整个供应链收益大幅下降的局面,且看涨期权折扣契约下降的幅度更大。为获取超额利润,决策者必须充分获取市场信息并对市场需求进行准确的预测才能使新的契约机制更有效。在新的前提条件下,看涨期权折扣契约模型能有效地协调供应链并提高整个供应链系统的绩效。该契约实现了风险共担和收益双赢,在一定程度上提升了供应链的柔性。     

State Dependent Pricing with a Queue

Existing studies of pricing when customers queue, assume that the firm cannot adjust the price to the state of demand. In most applications this assumption is false. We adapt the classic model of Naor (1969) to allow the firm to adjust the price to the state of demand. When customers are homogeneous the firm's pricing rule maximizes social welfare. When customers are unobservably heterogenous, the firm's pricing rule does not maximize social welfare. We find that the firm may not always attract customers even when it is technically and economically feasible to do so. This is interpreted as an option effect. The effects of changes to the basic parameters, on the queue length are presented.     

美式期权价格的积分表示及其数值方法

本文利用Laplace变换方法得到带连续红利的美式看涨期权价格的积分表示,以及最优执行边界满足的一个非线性的第二类Volterra积分方程.然后用数值积分公式给出了积分方程的数值解,从而得到了带连续红利的美式看涨期权价格及其执行边界的数值解.     

On the newsvendor model with conditional Value-at-Risk of opportunity loss

To manage the risk arising from uncertainty in market demand, this paper introduces the Conditional Value-at-Risk (CVaR) measure into the decision framework of the newsvendor who aims to minimise his opportunity loss. It is found under the CVaR measure that the newsvendor’s optimal order quantity is increasing in the confidence level when the understock loss is bigger than the overstock loss. This implies that an over-ordering may be even more caused by the newsvendor’s risk aversion about opportunity loss than risk seeking behaviour. Under this optimal order quantity, it is proved that the newsvendor’s expected profit and expected opportunity loss are decreasing and increasing in the confidence level, respectively. Furthermore, some management insights are presented to facilitate the risk management of the newsvendor model.     

美式期权价格的积分表示及其数值方法(英文)

本文利用Lalplace变换方法得到带连续红利的美式石看涨期权价格的积分表示,以及最优执行边界满足的一个非线性的第二类Volterra积分方程。然后用数值积分公式给出了积分方程的数值觯,从而得到了带连续红利的美式看涨期权价格及其执行边界的数值解。In this paper, we apply Laplace transform to obtain an integral representation for the solution for American call options with continuous dividend, and get a nonlinear Volterra integral equation of the second kind for the optimal exercise boundary. Then we give the numerical solution to the integral equation using the quadrature formulae, and so get the numerical solution of the price of American call option with continuous dividend and the optimal exercise boundary.     

时变变质率产品的订购-定价策略

研究时变变质率产品的订购与定价联合决策问题。以系统平均利润最大化为目标函数且将已变质产品的变质处理成本考虑在内,构建了相应的订购与定价联合决策模型,其中需求同时依赖于价格和库存水平、系统允许缺货且缺货量部分延迟订购。接着,对于已知的定价策略,证明并给出了最优补货策略唯一存在的充分条件;另一方面,对于已知补货策略的情况也证明了最优定价策略的存在性。此外,证明了在联合订购与定价决策下得到的最优销售价格总是大于单独进行定价决策时得到的最优价格。进而,在模型证明和分析的基础上给出一个寻求最优解的算法。最后,通过数值模拟的方法对模型中主要参数的灵敏度进行了分析,并给出相应的管理建议。结果表明：如果零售商忽略库存水平对需求的影响或变质处理成本,制定的销售价格将偏低;对于价格弹性较高的产品,零售商应采取低价销售策略;当顾客的等待耐心较差或产品的替代性较强时,最优策略应该是提高产品的销售定价并缩短缺货期。     

Supply chain coordination by risk sharing contracts under random production yield and deterministic demand

From numerous contributions to literature we know that properly designed contracts can facilitate coordinated decision making of multiple actors in a supply chain (SC) so that efficiency losses for the whole SC can be avoided. In a newsvendor-type SC with stochastic demand it is well-known that the double marginalization effect hampers the simple wholesale price contract to achieve coordination. More complex contracts however can bring about coordination, especially those which enable appropriate sharing of risks between the actors. While the effectiveness of risk sharing contracts is well understood for SC situations with random demand and reliable supply, less is known about respective problems if demand is deterministic but supply is unreliable due to random production yield. This paper shows how in a buyer-supplier SC the distribution of risks affects the coordination of buyer’s ordering and supplier’s production decision in a basic random yield, deterministic demand setting. Both parties are exposed to risks of over-production or under-delivery, respectively, if a simple wholesale price contract is applied. The resulting risk distribution always impedes SC coordination. However, more sophisticated contract types which penalize or reward the supplier can change risk distribution so that SC coordination is possible under random yield. Additionally, it is proven that the wholesale price contract will guarantee SC coordination if the supplier has a second (emergency) procurement source that is more costly, but reliable. Moreover, it is shown that under wholesale price contracts it can be beneficial to utilize this emergency source even if it is unprofitable from a SC perspective. However, if such an emergency option is available to the buyer as opposed to the supplier, a wholesale price contract will not be able to coordinate the SC.     

网络零售商产品与运费联合定价的优化决策研究

消费者网络购物对运费的认知和商家的偏好存在差异。通过消费者的购买行为分析和效用函数的刻画,研究网络零售商在进行产品与运费联合定价时捆绑定价和分割定价的优化决策问题。讨论商家之间价格竞争的组合形式,提出最优定价存在的情形选项,论证价格决策的边界和适用条件,揭示商家之间采用捆绑定价的对称竞争均衡具有稳定性,及其不同均衡条件下商家利润的相对大小规律。研究结论表明,价格决策的选项取决于商家的产品成本高低,在产品成本给定的条件下,每种价格决策的边界依赖于市场中消费者的属性特征,即运费存怀疑的消费者比例,以及消费者对商家的偏好程度。     

Review of supplier diversification and pricing strategies under random supply and demand

Uncertainties of supply and demand are two major sources of risk in any supply chain. As a result, the companies are implementing different strategies to mitigate the effects of these risks. Supplier diversification and responsive pricing are two of the main strategies that are used to mitigate the supply and demand risks. In supplier diversification, a firm uses multiple channels of sourcing while in responsive pricing, a firm manipulates demand through pricing to mitigate supply and demand risks. In this paper, we review lot-sizing problems when supply and demand are random. We focus on studies that have considered supplier diversification or responsive pricing as a mitigation strategy. We classify the studies based on their main assumptions and summarise their major findings. Finally, we present some directions for future research. Part of what we have found is that most studies that use multiple decision makers have focused on cases where information is complete and non-cooperative. There is a need to consider more realistic situations when there is information asymmetry between the decision makers. In addition, we have found that there is a lack of studies that look at the impact of joint ordering and pricing in the existence of multiple suppliers.     

幂型期权的保险精算定价(英文)

讨论了金融工程中的期权定价问题。在基础资产价格具有随机幅度跳跃的假设下,利用公平保费原理给出了幂型期权的保险精算价格。考虑到市场信息对风险资产价格影响的随机性,首先用一个具有随机跳跃幅度的跳扩散模型来刻画风险资产的价格过程,然后利用Poisson分布的性质和全期望公式导出了幂型期权的定价公式。在这个价格公式中公平的期权价格通过级数来表示,投资者因而可以容易地计算出期权价格,更好地管理价格风险。     

Risk hedging via options contracts for physical delivery

We develop an analytical framework for the valuation of options contracts for physical delivery that enable risk-sharing between the trading partners. The spot market price risk, the buyer's demand risk and the seller's marginal cost risk, which are key to many industrial settings such as the chemical industry, are explicitly incorporated. Analytical expressions for the buyer's optimal reservation quantity and the seller's optimal tariff are derived and related to the risk management needs in the industry. The ensuing discussion shows how contingency contracts for physical delivery can complement financial derivative instruments within a company's risk management approach.     

Pricing financial claims contingent upon an underlying asset monitored at discrete times

Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-transform in time and a Fourier transform in the logarithm of asset prices. The Wiener–Hopf technique is used to obtain probabilistic identities for the related random walks killed by an absorbing boundary. An accurate and efficient approximation is obtained using Padé approximants and an approximate inverse z-transform based on the trapezoidal rule. For simplicity, European barrier options in a Gaussian Black–Scholes framework are used to exemplify the technique (for which exact analytic expressions are obtained). Extensions to different option contracts and options driven by other Lévy processes are discussed.     

考虑风险偏好的定价决策与需求信息共享价值分析

为了分析零售商的风险偏好对定价决策及信息共享价值的影响,以期望利润与条件风险估值的加权平均作为目标准则来刻画零售商的决策目标函数,构建供应链的需求信息共享决策模型,通过该模型,深入地分析和研究零售商不同风险偏好下供应链的最优定价决策以及需求信息共享的价值。研究表明,信息不共享情况下最优批发价与λ无关;当市场不确定信息显示需求增加时,最优批发价、最优零售价、零售商信息共享价值随着λ的增大而增大,而供应商和供应链的信息共享价值随着λ的增大而减小;而当市场不确定信息显示需求减少时,最优批发价、最优零售价、零售商信息共享价值随着λ的增大而减小,而供应商和供应链的信息共享价值随着λ的增大而增大。     

Joint pricing and advertising strategy with reference price effect

Consumers are susceptible to reference price effects when they make purchase decisions for a certain product. Meanwhile, the sales price and advertisement are the determinable factors that have impact on consumers’ reference price which are also fundamental marketing strategies. Therefore, how to determine an appropriate sales price and advertising effort level to maximise firms’ profits is an essential task. A joint pricing and advertising problem for a monopolistic firm with consideration of reference price effect is investigated, where consumer demand rate is price-sensitivity and depends on the gap between the sales price and the reference price in consumers’ mind. An optimisation model is established to maximise the firm’s total profit by making a joint pricing and advertising strategy. The static and dynamic joint strategies are obtained by applying Pontryagin’s maximum principle. Results show that the dynamic strategies dominate the static ones. Furthermore, the dynamic pricing and dynamic advertising strategies are strategic complements. Additionally, the length of the sales period plays a key role in determining the superiority of the two dynamic strategies. Specifically, a relatively short sales period highlights the value of the dynamic advertising while a long sales period strengthens the function of the dynamic pricing.     

Optimal two-level piecewise-constant price discrimination for a storable perishable product

Price differentiation over time is an additional policy that firms might consider when determining prices for perishable products. The common policy of a fixed price regardless of freshness might result in leaving some expired inventory unsold. Price differentiation can impact the demand for perishable products, which declines as the expiration date approaches. We develop an optimisation model with the goal of evaluating the monetary effectiveness of the strategy of simultaneously combining price discrimination across heterogeneous consumers with price differentiation over time for perishable inventory under separable multiplicative demand factors of price and time. Necessary optimality equations are derived, and their solutions are proved to constitute a unique global optimal solution. It is proved that an optimal pricing policy is to implement price discrimination with respect to consumers’ sensitivity to freshness, while dynamically changing the price over time, starting with a lower price at the early stages of the product’s shelf life and increasing it at a later stage. The monetary benefit that the retailer and consumer can derive from the suggested pricing policy is evaluated by comparing the model to other models in which price discrimination or dynamic pricing are not implemented. A numerical example that illustrates the significance is introduced. From the analysis of a numerical illustration of the model, it is concluded that a dynamic price discrimination policy can be approximated by an identical-to-all dynamic pricing policy in order to maximise the retailer’s profit and thus, mitigate the retailer’s risk from failing in the process of implementing price discrimination.     

基于CVaR准则与ORP-RRP契约的闭环供应链决策模型

研究了基于预期订货量与实际回收量的回馈与惩罚ORP-RRP契约下的闭环供应链的协调问题。在CVaR准则下,提出了随机需求下单一风险厌恶型的零售商和单一风险中性的制造商组成的闭环供应链模型,探讨了供应链成员的决策行为、风险因子和废旧品回收敏感性系数;对废旧品回收价格和最优订货量的影响;研究结果表明：所建立的模型与ORP-RRP契约有效可行,可为供应链管理提供决策参考.