Equilibrium bandwidth and buffer allocations for elastic traffics

Consider a set of users sharing a network node under an allocation scheme that provides each user with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability and user demands. Equilibrium is achieved when all users optimize their utility and demand equals supply for nonfree resources. We analyze two models of user behavior. We show that at equilibrium expected return on purchasing variable resources can be higher than that on fixed resources. Thus users must balance the marginal increase in utility due to higher return on variable resources and the marginal decrease in utility due to their variability. For the first user model we further show that at equilibrium where such tradeoff is optimized all users hold strictly positive amounts of variable bandwidth and buffer. For the second model we show that if both variable bandwidth and buffer are scarce then at equilibrium every user either holds both variable resources or none

Congestion on risky routes with risk adverse drivers

We study the impact of information on risk adverse drivers who maximize their von Neumann and Morgerstern expected utility (rather than minimizing expected travel time). The preferences of the users are described by their utility functions. Beside the (potentially inconsistent) mean variance model used so far in transportation, we consider three other standard utility functions: the mean standard deviation model, and the CARA and CRRA utility functions. We show that maximization of expected utility provides a more general formulation than minimization of expected travel time (the latter case corresponds to the standard Wardrop principle). We illustrate the proposed approach with a simple network which consists in one origin/one destination and two routes in parallel. Total demand is inelastic. Capacity on one route is constant and on the other route it is stochastic, and depends on the states of nature, with two possible values. We assume that all users have the same value of time but that they differ in their risk aversion parameter. Equilibrium travel time then depends on the distribution of risk aversion. We consider two polar information regimes: no information and full information. We study the differential impacts of information according to the level of risk aversion, and compute the social value of information. We introduce a formula to compute the value of information that is the individual willingness to pay for information (or in economic terms, the compensating variation). Moreover, we find that optimal route choice may depend on global factors (and not only on local traffic conditions). This has serious implications on the design of driver information systems. Finally, we study road pricing when users are risk neutral (and minimize the expected travel time) and when users are risk adverse. We compare the level of tolls, as well as the benefits of road pricing with and without taking into account risk aversion.

Trading Volume in Dealer Markets

We develop a financial market trading model in the tradition of Glosten and Milgrom (1985) that allows us to incorporate non-trivial volume. We observe that in this model price volatility is positively related to the trading volume and to the absolute value of the net order flow, i.e. the order imbalance. Moreover, higher volume leads to higher order imbalances. These findings are consistent with well-established empirical findings. Our model further predicts that higher trader participation and systematic improvements in the quality of traders' information lead to higher volume, larger order imbalances, lower market depth, shorter duration, and higher price volatility.Market Microstructure, Trading Volume, Liquidity

Is It Is or Is It Ain't My Obligation? Regional Debt in a Fiscal Federation

This paper studies the repayment of regional debt in a multi-region economy with a central authority: who pays the obligation issued by a region? With commitment, a central government will use its taxation power to smooth distortionary taxes across regions. Absent commitment, the central government may be induced to bailout the regional government in order to smooth consumption and distortionary taxes across the regions. We characterize the conditions under which bailouts occur and their welfare implications. The gains to creating a federation are higher when the (government spending) shocks across regions are negatively correlated and volatile. We use these insights to comment on actual fiscal relations in three quite different federations: the US, the European Union and Argentina.

Unforeseen Contingencies

We develop a model of unforeseen contingencies. These are contingencies that are understood by economic agents - their consequences and probabilities are known - but are such that every description of such events necessarily leaves out relevant features that have a non-negligible impact on the parties' expected utilities. Using a simple co-insurance problem as a backdrop, we introduce a model where states are described in terms of objective features, and the description of an event specifies a finite number of such features. In this setting, unforeseen contingencies are present in the co-insurance problem when the first-best risk-sharing contract varies with the states of nature in a complex way that makes it highly sensitive to the component features of the states. In this environment, although agents can compute expected pay-offs, they are unable to include in any ex-ante agreement a description of the relevant contingencies that captures (even approximately) the relevant complexity of the risky environment.Unforeseen contingencies, incomplete contracts, finite invariance, fine variability.

A Continuation Multilevel Monte Carlo algorithm

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding weak and strong errors. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients

Is it is or is it ain't my obligation? Regional debt in a fiscal federation

This paper studies the repayment of regional debt in a multiregion economy with a central authority: Who pays the obligation issued by a region? With commitment, a central government will use its taxation power to smooth distortionary taxes across regions. Absent commitment, the central government may be induced to bail out the regional government in order to smooth consumption and distortionary taxes across the regions. We characterize the conditions under which bailouts occur and their welfare implications. The gains to creating a federation are higher when the (government spending) shocks across regions are negatively correlated and volatile. We use these insights to comment on actual fiscal relations in three quite different federations: the U.S., the European Union and Argentina.Taxation