2007 JFIG Paper Competition

First Place

Satisficing Measures for Analysis of Risky Positions
David Brown (Fuqua School of Business) and Melvyn Sim (National University of Singapore)

In this work we consider a class of measures for evaluating the quality of risky portfolios based on their performance relative to desired targets. We call these measures satisficing measures and show that they are dual to classes of corresponding risk measures. These dual descriptions have significant practical value in that they involve specifications of target or benchmark performance levels as opposed to risk tolerance parameters.

Second Place

Estimating Quantile Sensitivities
Jeff Hong (Hong Kong University of Science and Technology)

Quantiles of a random performance serve as important alternatives to the usual expected value. They play very important roles in risk management. For instance, they are used in financial industry as measures of capital adequacy and in service industry as measures of service quality. To control or optimize the quantile performance, we need to know how changes in the input parameters affect the output quantiles, which are called quantile sensitivities. In this paper we show that there exists a closed form of quantile sensitivity, which is in the form of a conditional expectation. Based on this form, we first propose an infinitesimal-perturbation-analysis (IPA) estimator. The IPA estimator is asymptotically unbiased, but it fails to be consistent. We then obtain a consistent estimator by dividing data into batches and averaging the IPA estimates of all batches. We also show that the estimator satisfies a central limit theorem for the i.i.d. data. Therefore, the confidence intervals of the estimator can be constructed. The numerical results show that the proposed estimator and confidence intervals work well for practical problems.

Finalists

Public Evacuation Decisions and Hurricane Track Uncertainty
Eva Regnier (Naval Postgraduate School)

Public officials with the authority to order hurricane evacuations face a difficult trade-off between risks to life and costly false alarms. Evacuation decisions must be made on the basis of imperfect information, in the form of forecasts. The quality of these decisions can be improved if they are also informed by measures of uncertainty about the forecast, including estimates of the value of waiting for updated, more accurate, forecasts. Using a stochastic model of storm motion derived from historic tracks, this paper explores the relationship between lead time and track uncertainty for Atlantic hurricanes, and the implications of this relationship for evacuation decisions. Typical evacuation clearance times and track uncertainty imply that public officials who require no more than a 10% probability of failing to evacuate before a striking hurricane (a false negative) must accept that at least 76%–and for some locations over 90%–of evacuations will be false alarms. Reducing decision lead times from 72 to 48 hours for major population centers could save an average of hundreds of millions of dollars in evacuation costs annually, with substantial geographic variation in savings.

Customer Herding in Queues: Inferring Service Quality from Queue Lengths
Senthil Veeraraghavan (The Wharton School) and Laurens Debo (Carnegie Mellon University)

A classic example that illustrates how observed customer behavior impacts other customers’ decisions is the selection of a restaurant whose quality is uncertain: Customers often choose a busier restaurant, inferring that other customers in that restaurant know something that they do not know. In an environment with random arrival and service times, customer behavior is reflected in the queue lengths. Queue lengths could signal two factors - potentially higher arrival rates to the server or potentially slower service rate at the server. We focus on the effect of potentially higher arrival rates at a server on the choices of other customers. Rational customers that observe queue lengths at different service providers will complement their private information about the quality of each service provider with the information they obtain from the queue lengths. In this paper, we study how a market is split between two comparable service providers when there are externalities due to the queue lengths that customers observe. Customers arrive according to a Poisson process to the market. Service times are exponentially distributed with the same rate at each service provider. Based on both private information about the service quality and queue length information, customers decide which queue to join. We find that it may be rational in equilibrium to ignore private information completely and purchase from the service provider with the longer queue. Further, we show that such choice behavior causes temporary successful periods for a firm. Such periods might alternate with periods when the firm does not receive any customers. We show that a firm that provides higher valuation of service is more likely to succeed in getting more customers. Finally, we also capture the value of information due to congestion in markets where competing services have uncertain quality.

Network Design and Allocation Mechanisms for Carrier Alliances in Liner Shipping
Ozlem Ergun (Georgia Tech) and Richa Agarwal (Georgia Tech)

Many real world systems operate in a decentralized manner, where individual operators interact with varying degree of cooperation and self motives. In this paper, we study transportation networks that operate as an alliance among different carriers. In particular, we study alliance formation among carriers in liner shipping. We address tactical problems such as the design of large scale networks (which result from integrating the service networks of different carriers in an alliance) and operational problems such as the allocation of limited capacity on a transportation network among the carriers in the alliance. We utilize concepts from mathematical programming and game theory and design a mechanism to guide the carriers in an alliance to pursue an optimal collaborative strategy. The mechanism provides side payments to the carriers, as an added incentive, to motivate them to act in the best interest of the alliance while maximizing their own profits. Our computational results suggest that the mechanism can be used to help carriers form sustainable alliances.

Eliciting Coordination with Rebates
Nicolas Stier-Moses (Columbia Business School) and Patrick Maille (GET/ENST France)

This article considers network routing games, which can readily be used to model competition in telecommunication, traffic, transit or distribution networks. We study a mechanism based on rebates that provides incentives for participants to cooperate. This mechanism is modeled by a Stackelberg game in which the system owner offers rebates, and participants select their routes considering the rebates. The system owner decides how much to offer taking into account both the potential participants’ cost reduction as well as the cost of providing those rebates. Indeed, the re- bate budget may come from the savings that arise from the more efficient solution. We characterize the Stackelberg equilibria of the game, and describe a polynomial-time algorithm to compute the optimal rebates. In addition, we provide tight results on their worst-case inefficiency measured by the so-called price of anarchy. Specifically, we describe the tradeoff between the sensitivity of the owner towards rebate costs and the worst-case inefficiency of the system.