Optimal Selling of an Asset with Jumps Under Incomplete Information

ABSTRACT

We study the optimal liquidation strategy of an asset with price process satisfying a jump diffusion model with unknown jump intensity. It is assumed that the intensity takes one of two given values, and we have an initial estimate for the probability of both of them. As time goes by, by observing the price fluctuations, we can thus update our beliefs about the probabilities for the intensity distribution. We formulate an optimal stopping problem describing the optimal liquidation problem. It is shown that the optimal strategy is to liquidate the first time the point process falls below (goes above) a certain time-dependent boundary.     

不允许卖空的组合投资决策

本建立了一定置信水平下最小收益最大准则下的组合投资决策模型，该模型不仅适用于风险规避，也适用于风险偏好，在风险资产的收益率联合服从正态分布的假设下，给出不容许卖空情形下的求解有效资产组合的算法，并给出一个算例。     

Optimal Decision Rules for Producing Greeting Cards

A first attempt at applying OR techniques and approaches in a fine art printing firm manufacturing greeting cards is reported in this paper. The problem of economic production of cards is formulated and four related methods are presented, the fourth being a probabilistic model with possibly wider applications in the fashion industry     

考虑线下渠道时销售商在团购网站上的最优销售策略研究

基于团购网站和销售商的典型合作模式,考虑了团购网站和线下市场的相互影响,用非线性优化理论为基础以销售商制定团购上限和团购项目定价为决策变量,考虑团购价格和最低团购数量的约束条件,建立模型优化,求解出销售商推出团购项目的最优策略。考虑到团购网站下限和团购网站销售成本以及网上销售的广告效用,分析了销售商是否应该制定团购上限,如何结合团购项目定价制定团购上限。探讨了在线低价限量销售的优势,以及顾客转移购买率和团购下限对销售商策略选择的影响。通过和单一线下渠道的最优销售策略相比较,得出销售商推出团购项目的前提条件。同时为团购网站运营商如何引导销售商推出低价团购项目提供了管理启示。     

渐近最优的经验贝叶斯决策

本文在加权线性损失下讨论一类广义指数分布刻度参数的经验贝叶斯检验问题.利用核密度估计函数构造单调的经验贝叶斯检验函数,在适当的条件下证明所构造的检验函数的渐近最优性并获得其收敛速度.该收敛速度可以任意接近O(n-1).最后,给出一个例子用以验证本文的主要结果是合理的.     

渐近最优的经验贝叶斯决策

本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性.     

销售率线性依赖瞬时库存水平的两货栈决策模型

在成熟期的存货影响销售环境下,考虑销售率线性依赖瞬时库存水平,不允许缺货,研究了一类非变质性物品的两货栈库存决策问题.建立了以系统平均总利润最大为目标的决策模型,分析了系统最优库存策略的存在性和唯一性,并给出了求解模型的有效方法.分析结果表明,库存管理者利用租用货栈进行订货决策时,除了要充分考虑企业自身的库存容量外,还取决于自有货栈产品相关参数对库存系统绩效的边际贡献率.     

一类产品分批销售数量的优化策略

在价格和需求不确定的情况下,本文研究对一类固定容量的非易逝品进行分批销售的数量优化问题.假定各阶段的需求为价格敏感的且相互独立,在最大化期望折扣总收益的目标下,我们为该问题分别建立了有限阶段和无限阶段模型,并讨论了模型的最优解的存在性及有关解的结构性质;然后,通过数值分析进一步验证了理论分析的结果,同时还讨论了几个系统参数对最优策略及最优收益值的影响;最后结合理论和数值分析的结果,我们发现:产品分批销售时的最优预售数量随当前价格和剩余产品的数量非降,而随剩余的销售时间非增.     

一类时变需求且存货影响销售率的EOQ模型

从实际背景出发,在R AM P型需求和存货影响销售率条件下,讨论了一类以缺货开始的变质性物品的EOQ模型.给出了模型的求解方案及单位时间内平均利润最大化的两个充分条件,并用数值算例进行了验证.     

企业最优投资决策研究

提高企业效益的一个很重要方面是提高企业的投资效益.针对这一问题,运用动态规划的方法,提出了一个决策模型,使该模型得出的投资方案产生最大的贴现现金流(DCF).     

具有随机需求量的存货决策分析方法

陶菊春、吴建民．具有随机需求量的存货决策分析方法．数理统计与管理，１９９８，１７（４），２８～３２．本文讨论了具有随机需求量的存货决策分析方法。着重分析了订购批量和再订购点的确定问题，得出了需求量为常用分布的再订购点的计算公式以及需求量的分布未知时，再订购点的估计式。最后，通过例子说明了具有随机需求量的存货决策程序。     

Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson process. The problem is a nonstandard mixed discrete/continuous optimal control problem, which we face by the dynamic programming approach. The main goal of the paper is the characterization of the value function as unique viscosity solution of an associated Hamilton–Jacobi–Bellman equation. We then use such a result to build a numerical algorithm, allowing one to approximate the value function and so to measure the cost of illiquidity.     

基于电商平台的最优销售模式和退款保证策略研究

基于一个制造商和一个平台商组成的供应链,考虑消费者退货行为,运用博弈论建立了不同销售模式和退款保证策略下的六个模型。通过均衡解对比和数值算例分析,给出了制造商的最优销售模式选择和制造商与平台商的退款保证策略。研究发现:制造商同时选择转售和代理模式对其自身、平台商和消费者都最有利;在制造商同时选择两种销售模式的情况下,当转售和代理模式下客户满意度都比较高时,佣金费率对制造商和平台商的退款保证策略选择没有影响,制造商始终倾向于提供退款保证而平台商始终倾向于不提供退款保证。     

利用模糊优选技术进行证券投资价值决策分析

本根据多属性决策的基本理论,利用模糊优选技术研究了证券价值决策问题,提出了相对投资价值与当前价格相结合的分析方法,并进行了实例分析。     

A Binary Decision Model for the Stock Control of Very Slow Moving Items

In this note a model for very slow moving items is developed in order to decide whether it is economic to have 0 or 1 item in stock. The model is applied to a real situation and substantial savings are obtained.     

永久经理期权的最优实施策略

利用偏微分方程数值方法研究金融市场上永久经理期权(ESOs)的最优实施策略问题.讨论了两种实施情况,即通常的整体实施情况以及非限制实施情况.在非限制实施情况下,持有者在任意可实施时刻可以实施其持有的任意份ESOs.两种实施情况下的最优实施策略分别对应着一个抛物型变分不等式定解问题的自由边界(最佳实施边界).通过数值分析的方法分别研究了自由边界的性质,比较了两种情况下自由边界的异同及其所对应的金融意义.     

Optimal Die Stock Control at Firth Vickers Foundry

This case study emphasises the growing importance of management sciences, operational research, and computing in the decision-making processes of production management in a dynamic high-technology company. The study is concerned with a computer system for die stock control and selection developed in conjunction with the management of Firth Vickers Foundry, Sheffield, following an initial diagnostic survey to define the problem and outline a solution to it. This article describes the effect on production costs (melting, spinning, machining and die costs) of the system which is designed to enable management to exercise optimal control of die stocks in the centri-spinning section of the foundry. The approach to the problem and development of logic are, however, applicable to all fluid-to-solid process industries where differently sized regular moulds or dies are stocked to meet order patterns of variable dimensions.     

多属性决策中的一种最优组合赋权方法研究

在多属性决策中权系数的确定是非常重要的。从最大地利用信息这个角度，综合各种赋权法的特点，以离差平方和为准则建立了最优组合赋权模型。并以实例表明该方法有效性。     

A Decision Criterion for the Optimal Number of Clusters in Hierarchical Clustering

Clustering has been widely used to partition data into groups so that the degree of association is high among members of the same group and low among members of different groups. Though many effective and efficient clustering algorithms have been developed and deployed, most of them still suffer from the lack of automatic or online decision for optimal number of clusters. In this paper, we define clustering gain as a measure for clustering optimality, which is based on the squared error sum as a clustering algorithm proceeds. When the measure is applied to a hierarchical clustering algorithm, an optimal number of clusters can be found. Our clustering measure shows good performance producing intuitively reasonable clustering configurations in Euclidean space according to the evidence from experimental results. Furthermore, the measure can be utilized to estimate the desired number of clusters for partitional clustering methods as well. Therefore, the clustering gain measure provides a promising technique for achieving a higher level of quality for a wide range of clustering methods.     

摩擦市场中最优证券组合选择的极大极小法

在考虑交易成本的基础上,构造最优投资组合选择的极大极小模型,同时允许投资者卖空风险资产.在求解过程中,针对出现的非光滑函数,通过引入极大熵函数用光滑问题来逼近非光滑问题.最后推导出连续可微的方程组,可采用经典牛顿法求解.数值分析验证了该方法的有效性.