Study Of Some Pricing Problem In Stochastic Environment

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.