【作者】 魏轶华；

【导师】 胡奇英；

【作者基本信息】 西安电子科技大学 ， 应用数学， 2004， 博士

【摘要】 随机环境下的定价研究在营销学中有着重要的地位与作用，并已经取得了一定的成就，但还有相当多的问题有待于进一步的研究。本文对以下三类随机环境下的定价模型进行了研究：存贮定价、连续时间收益管理以及电力市场中的拍卖。主要内容如下。 (1) 考虑容量决策的多阶段存贮定价问题。分析了折扣准则下单产品的多阶段存贮、定价及容量扩张问题。建立了马氏决策过程模型，首先对有限阶段问题进行了研究，得到了其最优策略。进一步，对无限阶段情况下的存贮定价问题进行了讨论。 (2) 连续时间收益管理模型。分别研究了单商品和多商品问题。对于单商品问题的研究又分为两部分：顾客具有最大、最小保留价的连续时间收益管理问题，和具一般需求函数和价格集合的连续时间收益管理问题。对顾客具有最大、最小保留价的连续时间收益管理模型问题，得到了最大期望收益函数单调性及凹性、最优策略的单调性、以及最大期望收益函数的上、下界。对具一般需求函数和价格集合的连续时间收益管理模型，我们证明了它可以等价为一个与上面模型形式相同的模型，从而上面的结论依然成立。对于多产品连续时间收益管理问题，我们通过最优值函数的所满足的一个微分方程构造出了离散价格集下零售商的最优报价策略和最大期望收益函数。 (3) 连续时间收益管理的进一步探讨。进一步探讨了收益管理问题。主要分为两个部分：容量约束对收益的影响和竞争情况下的连续时间收益管理。在容量约束方面，分别考虑了寡头垄断市场和连续时间收益管理时的情况。结果表明，通过最优的定价决策，非最优容量带来的收益损失并不是很大。在竞争连续时间收益管理方面，建立了一个一级价格密封拍卖的连续时间收益管理模型，证明了其最大期望收益的单调性及凹性以及最优报价策略的单调性，并得出了最大期望收益的上界。 (4) 电力定价：密封拍卖模型Ⅰ(简单拍卖)。研究了电力市场中简单拍卖的三个问题；出清价格拍卖，序贯拍卖和二级价格密封拍卖中的欺骗报价。在出清价格拍卖方面，得到了投标人的最优报价策略，并进一步对投标人搜集私有信息的决策进行了讨论。在序贯拍卖方面，分别讨论了一级价格序贯拍卖和二级价格序贯拍卖：对一级价格序贯拍卖，得出投标人最优报价策略所满足的微分方程；对二级价格序贯拍卖，得到了投标人最优报价策略。进一步，针对投标人为风险中性、风险寻求和风险厌恶三种情况进行了具体讨论.对二级价格密封拍卖中的欺骗报价，得到了投标人的最优报价策略，并证明在T次序列拍卖中拍卖人的最优拍卖机制选择策略是一个吞阶段策略. (s)电力定价:密封拍卖模型11(复杂拍卖).研究了电力市场中的三种复杂拍卖:一级价格密封拍卖、出清价格拍卖和二级价格密封拍卖.对每种拍卖规则，又分电力公司不补偿购买超额供给电量和补偿购买超额供给电量两种情况进行了具体分析，建立了投标人的博弈模型，并得到了投标人的最优报价策略. 关键词:定价随机环境存贮连续时间收益管理HJB方程电力市场密封拍卖更多还原

【Abstract】 The study of pricing in stochastic condition plays a important role in marketing, and a series of achievements have been obtained in this field, but there still exist many problem need to be studied. This paper studies the following three stochastic pricing problems: combining pricing, inventory and capacity expansion; continuous time revenue management; sealed-bid auctions in power market. The main content are listed as follows.(1) Multi-period model combining pricing, inventory and capacity expansion. Firstly, we discuss the inventory and pricing and capacity strategies of a single item with periodic review. By using of Markov Decision Process, the finite horizon inventory, pricing and capacity expansion problem is discussed, and the optimal strategy of which is obtained. In succession, we discuss the problem in infinite horizon.(2) Continuous time revenue management. One-item problem and multi-item problem are both discussed respectively. And two problems are discussed in one-item case: continuous time revenue management with maximal and minimal reservation prices and; continuous time yield management model with general demand function and price set. For the continuous time revenue management model with maximal and minimal reservation, we show that the optimal expected revenue of the retailer is increasing and concave in the number of items to be sold and the time remained respectively, and the optimal pricing policy is decreasing in the number of items to be sold and increasing in the time remained. A bound on the optimal expected revenue is also obtained. For the continuous time yield management model with general demand function and price set, we show the above conclusion is still come into existence. For the multi-item continues time problem, by use of a differential function that the optimal value function satisfies, we construct the retailer’s optimal price policy and maximal expected revenue function in case of discreet price set.(3) Advance study of revenue management. Contains two part: capacity restriction of perishable assets, and continues time revenue management in competition condition. For the capacity restriction problem, we show that although capacity is uncontrollable, but with the optimal pricing policy, it has a minor influence on profits. For the competitive continues time revenue management problem, a first price-sealed auction continues time revenue management model is constructed, and the increasing and concave property of the maximal expected revenue, the monotony property of the optimal price policy, and the up-bound of the maximal expected revenue are both obtained.(4) Simple bid in power market. There problems are discussed: clearing price auctions, sequential auctions, and cheating bids in the second-price sealedauction. For clearing price auctions, the optimal bidding strategy of the bidder is obtained, and the effect of a bidder’s private information on his profit and other bidders’ profit is studied. For sequential auctions, With the first price rule, we obtain a differential function for the optimal bidding strategy; with the second price rule, the optimal bidding strategy is obtained. And we discuss this problem in detail in case of bidders are: risk neutral, risk aversion, and risk seeking. For the cheating bids in the second-price sealed auction, the bidder’s optimal bidding strategy is obtained, and we show that the auctioneer’s optimal policy is a t-stage policy.(5) Complex bid in power market. Three kinds of complex bid is studied: first price sealed-bid auction, second price sealed-bid auction, and clearing price auction. For each auction rule, we discuss the problem in case of the power company purchases the overage supply power or not respectively, the bidder’s game model is constructed, and the bidder’s optimal biding strategy is obtained.更多还原