具有随机寿命的二维期权定价

由于期权合约在到期日之前可能被终止及标的资产的价格可能会因重大信息的到达而发生跳跃 ,文中在假设合约被终止的风险与重大信息导致的价格跳跃风险皆为非系统的风险情况下 ,应用无套利资本资产定价及Feynman kac公式 ,首先研究了标的资产服从连续扩散过程和跳—扩散过程具有随机寿命的交换期权定价 ,得到相应的定价公式 ;然后 ,研究了标的资产服从跳—扩散过程及利率随机变化具有随机寿命的期权定价 ,得到相应的定价公式     

可转换债券的复合期权定价模型

可转换债券是一种内含期权结构的特殊金融产品。可转换债券的内含期权是一种奇异期权——复合期权。本文通过分别对无期权债券和复合期权的定价，获得了可转换债券在风险中性条件下的定价模型。     

基于实物期权的军队油库设备投资改造决策模型研究

利用实物期权的投资决策理论对军事油库设备改造进行了探讨,针对投资项目所具有的时间选择期权和放弃期权的混合特征,根据决策树的思想,采用二项式期权定价理论和不确定规划方法,构造了一种以战略净现值最大化为投资目标的军队油库设备投资决策模型。该模型有效地评估了投资机会的价值,解释了投资者时机选择和投资期限决策行为,有助于提高油库资金的军事效益和经济效益。     

证券组合保险业务的兴衰

金融工程是一门将金融经济学、数学、计算技术及科学方法应用于金融资产的获得、运用和保护的学科。70年代初期,麻省理工学院的研究工作导致布莱克-舒尔茨-默顿期权定价公式的出现,标志着金融工程学的诞生。在麻省理工学院开展期权定价理论研究工作的同时,芝加哥大学、兰德公司、加州大学洛杉矶分校等单位的学者则在开展金融工程的另一个分支的研究工作──风险分析、证券     

P(r)P振子的自由振动频率规律性研究

将恢复力为ε·sign(x)·|x|~r的振子命名为具有单纯r次幂型恢复力的振子,记为P(r)P振子,给出了其自由振动频率的精确计算公式。提出了频率幂次常数和当量刚度等概念,将P(r)P振子自由振动频率归纳为频率幂次常数与当量刚度平方根的乘积。提出了P(r)P振子的分类方法:把幂次r在0和1之间的称为渐柔型P(r)P振子,振幅愈大,其自由振动频率愈小;幂次r大于1的称为渐刚型P(r)P振子,其自由振动频率随振幅的增大而增大。     

武器装备研制投资决策方法研究

文章分别对武器装备研制投资决策的传统方法与实物期权方法进行研究，针对实物期权方法在武器装备研制投资决策中的应用研究现状，提出实物期权方法在武器装备研制投资决策中的应用问题需要进一步系统地研究。     

关于旋进椭圆的讨论

本文采用作用角变量的方法,讨论了闭合轨道在一般幂次型引力势作用下的情况。采用这种方法时,初始轨道接近于圃轨道的假设是不必要的,而且引力势的形式可以推广到平方反比力场和其它幂次力场。文中给出了轨道闭合的判别公式。若中心力包括r~(-2)项和r~(-3)项时,即相对论校正情况,则轨道闭合成为旋进椭圆;它的旋进角速度可以计算出来。     

倒向随机微分方程在欧式期权中的应用

假设市场为无套利市场,而且市场上只有两种证券:一种是无风险债券;一种是有风险的股票。通过自筹资策略,得到期权价格所满足的倒向随机微分方程(BSDE),利用倒向随机微分方程给出欧式期权价格概率表示;并证明欧式期权的完全套期保值性。     

Cache计时攻击对E1Gamal签名的安全威胁分析

分析了E1Gamal签名中模幂运算的平方乘算法和滑动窗口算法,给出了两种算法下利用Cache计时采集旁路信息的方法和幂指数恢复算法,分析了Cache计时攻击对幂指数相关的旁路信息获取能力以及Cache计时攻击对E1Gamal签名的安全性威胁．通过仿真验证了Cache计时攻击能够有效获取旁路信息,展示了不同长度随机密钥的安全等级,给出了建议采用的随机密钥长度与可能的防御措施．     

一类扩散过程的最优停止

金融数学中关于美式期权的定价理论最后归结为一个对扩散过程的最优停止问题,扩散过程是特殊的马氏过程,本文讨论了当报酬函数非负时的值函数性质及其最优停时的表示。特别对带折扣的报酬的讨论,更加符合金融数学的需要     

Vertically restrictive pricing in supply chains with price‐dependent demand

We examine the behavior of a manufacturer and a retailer in a decentralized supply chain under price‐dependent, stochastic demand. We model a retail fixed markup (RFM) policy, which can arise as a form of vertically restrictive pricing in a supply chain, and we examine its effect on supply chain performance. We prove the existence of the optimal pricing and replenishment policies when demand has a linear additive form and the distribution of the uncertainty component has a nondecreasing failure rate. We numerically compare the relative performance of RFM to a price‐only contract and we find that RFM results in greater profit for the supply chain than the price‐only contract in a variety of scenarios. We find that RFM can lead to Pareto‐improving solutions where both the supplier and the retailer earn more profit than under a price‐only contract. Finally, we compare RFM to a buyback contract and explore the implications of allowing the fixed markup parameter to be endogenous to the model. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

Optimal power control in a wireless network using a model with stochastic link coefficients

This paper addresses optimal power allocation in a wireless communication network under uncertainty. The paper introduces a framework for optimal transmit power allocation in a wireless network where both the useful and interference coefficients are random. The new approach to power control is based on a stochastic programming formulation with probabilistic SIR constraints. This allows to state the power allocation problem as a convex optimization problem assuming normally or log‐normally distributed communication link coefficients. Numerical examples illustrate the performance of the optimal stochastic power allocation. A distributed algorithm for the decentralized solution of the stochastic power allocation problem is discussed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Spatial pricing and product allocation in online retailing

Spatial pricing means a retailer price discriminates its customers based on their geographic locations. In this article, we study how an online retailer should jointly allocate multiple products and facilitate spatial price discrimination to maximize profits. When deciding between a centralized product allocation ((i.e., different products are allocated to the same fulfillment center) and decentralized product allocation (ie, different products are allocated to different fulfillment centers), the retailer faces the tradeoff between shipment pooling (ie, shipping multiple products in one package), and demand localization (ie, stocking products to satisfy local demand) based on its understanding of customers' product valuations. In our basic model, we consider two widely used spatial pricing policies: free on board (FOB) pricing that charges each customer the exact amount of shipping cost, and uniform delivered (UD) pricing that provides free shipping. We propose a stylized model and find that centralized product allocation is preferred when demand localization effect is relatively low or shipment pooling benefit is relatively high under both spatial pricing policies. Moreover, centralized product allocation is more preferred under the FOB pricing which encourages the purchase of virtual bundles of multiple products. Furthermore, we respectively extend the UD and FOB pricing policies to flat rate shipping (ie, the firm charges a constant shipping fee for each purchase), and linear rate shipping (ie, the firm sets the shipping fee as a fixed proportion of firm's actual fulfillment costs). While similar observations from the basic model still hold, we find the firm can improve its profit by sharing the fulfillment cost with its customers via the flat rate or linear rate shipping fee structure.     

Dynamic pricing in a dual‐market environment

This article is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, for example, a long‐distance market and an on‐site market. The key difference between the two markets is that the long‐distance market provides for a one period delay in demand fulfillment. In contrast, on‐site orders must be filled immediately as the customer is at the physical on‐site location. We model the demands in consecutive periods as independent random variables and their distributions depend on the item's price in accordance with two general stochastic demand functions: additive or multiplicative. The firm uses a single pool of inventory to fulfill demands from both markets. We investigate properties of the structure of the dynamic pricing strategy that maximizes the total expected discounted profit over the finite time horizon, under fixed or controlled replenishment conditions. Further, we provide conditions under which one market may be the preferred outlet to sale over the other. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 531–549, 2015     

Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

On efficiency of multistage channel with bargaining over wholesale prices

This article considers a multistage channel with deterministic price‐sensitive demand. Two systems for pricing decisions, that is, the bargaining system and the leader‐follower system, are compared. We characterize the necessary and sufficient conditions on the power structure, under which the solution of the bargaining system Pareto dominates that of the leader‐follower system. Also, under such conditions, we give a tight upper bound of channel efficiency of the bargaining system, which converges to 100% channel efficiency as the number of stages increases to infinity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 449–459, 2016     

中国收费公路制度改革的利益机制设计

收费公路是我国市场化改革延伸到基础设施的重大举措。收费公路已经被作为一种商品在向市场提供,且公路特殊性,使得收费公路产业具有明显的自然垄断性。在公路收费定价优势信息的主导下,在收费公路定价方面通行者处于明显劣势地位。本文希望通过利益机制的设计来提升通行者在收费公路定价博弈中的地位,通过利益机制设计中的激励与约束使公路收费定价者会倾向于选择更公平、公正的价格。