Motivated from second-order stochastic dominance, we introduce a risk measure that we call shortfall. We examine shortfall's properties and discuss its relation to such commonly used risk measures as standard deviation, VaR, lower partial moments, and coherent risk measures. We show that the mean-shortfall optimization problem, unlike mean-VaR, can be solved e ciently as a convex optimization problem, while the sample mean-shortfall portfolio optimization problem can be solved very e ciently as a linear optimization problem. We provide empirical evidence (a) in asset allocation, and (b) in a problem of tracking an index using only a limited number of assets that the mean-shortfall approach might have advantages over mean-variance. ?

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Advanced traveler information systems (ATISs) are being developed to provide travelers with real-time information about traffic conditions. To evaluate the benefits of ATIS products and services, questions concerning the potential market, use, and travel response must be addressed. The present focus is on the en-route travel response to ATISs. The main objective is to explore how travelers deal with unexpected congestion and how they might respond to qualitative, quantitative, prescriptive, and predictive information. Data on travelers' route-switching decisions were obtained through a survey of California Bay Area automobile commuters. The effects of various factors, such as sources of congestion information (radio traffic reports versus observation), trip characteristics, and route attributes on traveler response to unexpected congestion, were investigated. Future response to ATIS technologies was explored by using stated preferences, that is, hypothetical ATIS scenarios. A combined reported and stated preference model of traveler response was developed. The results indicate that expected delays on the usual route, travel time on alternative routes, perceived congestion level on alternative routes, and information sources are important determinants of travel decision changes in response to unexpected delays. The modeling methodology identifies the effects of experience and behavioral inertia on choices and captures inherent biases in the stated preference responses. Overall, travelers are more likely to respond to specific quantitative delay information.