On martingale measures when asset returns have unpredictable jumps

AbstractWe study financial market incompleteness induced by discontinuities in asset returns. When there are multiple outcomes for a discontinuity, it is shown that this incompleteness cannot be removed by the introduction of extra securities. Claims cannot be hedged and are thereby not uniquely priced by arbitrage. We characterize the family of martingale measures associated with this form of incompleteness and discuss issues of existence and uniqueness for important special cases. Finally, using methods of stochastic control, we apply these results to derive replicating policies for arbitrary contingent claims and thereby relate the prices of contingent claims to the family of measures

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102647/1/poms12047.pd

Newsvendor bounds and heuristics for serial supply chains with regular and expedited shipping

We study an infinite-horizon, N -stage, serial production/inventory system with two transportation modes between stages: regular shipping and expedited shipping. The optimal inventory policy for this system is a top–down echelon base-stock policy, which can be computed through minimizing 2 N nested convex functions recursively (Lawson and Porteus, Oper Res 48 (2000), 878–893). In this article, we first present some structural properties and comparative statics for the parameters of the optimal inventory policies, we then derive simple, newsvendor-type lower and upper bounds for the optimal control parameters. These results are used to develop near optimal heuristic solutions for the echelon base-stock policies. Numerical studies show that the heuristic performs well. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/64894/1/20388_ftp.pd

Optimal Uniform Pricing Strategy of a Service Firm When Facing Two Classes of Customers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106838/1/poms12171.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/106838/2/poms12171-sup-0001-Onlinesupplement.pd

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109985/1/poms12221-sup-0001-OnlineSupplement.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/109985/2/poms12221.pd

Optimal Reserve Prices in Name-Your-Own-Price Auctions with Bidding and Channel Options

Few papers have explored the optimal reserve prices in the name-your-own-price (NYOP) channel with bidding options in a multiple channel environment. In this paper, we investigate a double-bid business model in which the consumers can bid twice in the NYOP channel, and compare it with the single-bid case. We also study the impact of adding a retailer-own list-price channel on the optimal reserve prices. This paper focuses on achieving some basic understanding on the potential gain of adding a second bid option to a single-bid system and on the potential benefits of adding a list-price channel by the NYOP retailer. We show that a double-bid scenario can outperform a single-bid scenario in both single-channel and dual-channel situations. The optimal reserve price in the double-bid scenario is no less than that in the single-bid case. Furthermore, the addition of a retailer-own list-price channel could push up the reserve prices in both single-bid and double-bid scenarios

Optimal Reserve Prices in Name-Your-Own-Price Auctions with Bidding and Channel Options

Few papers have explored the optimal reserve prices in the name-your-own-price (NYOP) channel with bidding options in a multiple channel environment. In this paper, we investigate a double-bid business model in which the consumers can bid twice in the NYOP channel, and compare it with the single-bid case. We also study the impact of adding a retailer-own list-price channel on the optimal reserve prices. This paper focuses on achieving some basic understanding on the potential gain of adding a second bid option to a single-bid system and on the potential benefits of adding a list-price channel by the NYOP retailer. We show that a double-bid scenario can outperform a single-bid scenario in both single-channel and dual-channel situations. The optimal reserve price in the double-bid scenario is no less than that in the single-bid case. Furthermore, the addition of a retailer-own list-price channel could push up the reserve prices in both single-bid and double-bid scenarios.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78715/1/j.1937-5956.2009.01045.x.pd

Dynamic Customer Acquisition and Retention Management

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134194/1/poms12559.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134194/2/poms12559_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134194/3/poms12559-sup-0001-Appendix.pd

Dynamic inventory control with limited capital and short‐term financing

For most firms, especially the small‐ and medium‐sized ones, the operational decisions are affected by their internal capital and ability to obtain external capital. However, the majority of the literature on dynamic inventory control ignores the firm's financial status and financing issues. An important question that arises is: what are the optimal inventory and financing policies for firms with limited internal capital and limited access to external capital? In this article, we study a dynamic inventory control problem where a capital‐constrained firm periodically purchases a product from a supplier and sells it to a market with random demands. In each period, the firm can use its own capital and/or borrow a short‐term loan to purchase the product, with the interest rate being nondecreasing in the loan size. The objective is to maximize the firm's expected terminal wealth at the end of the planning horizon. We show that the optimal inventory policy in each period is an equity‐level‐dependent base‐stock policy, where the equity level is the sum of the firm's capital level and the value of its on‐hand inventory evaluated at the purchasing cost; and the structure of the optimal policy can be characterized by four intervals of the equity level. Our results shed light on the dynamic inventory control for firms with limited capital and short‐term financing capabilities.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 184–201, 2014Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106828/1/nav21576.pd

Capacity expansion and cost efficiency improvement in the warehouse problem

The warehouse problem with deterministic production cost, selling prices, and demand was introduced in the 1950s and there is a renewed interest recently due to its applications in energy storage and arbitrage. In this paper, we consider two extensions of the warehouse problem and develop efficient computational algorithms for finding their optimal solutions. First, we consider a model where the firm can invest in capacity expansion projects for the warehouse while simultaneously making production and sales decisions in each period. We show that this problem can be solved with a computational complexity that is linear in the product of the length of the planning horizon and the number of capacity expansion projects. We then consider a problem in which the firm can invest to improve production cost efficiency while simultaneously making production and sales decisions in each period. The resulting optimization problem is nonâ convex with integer decision variables. We show that, under some mild conditions on the cost data, the problem can be solved in linear computational time. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 367â 373, 2016Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134190/1/nav21703_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134190/2/nav21703.pd