Non-peaky signals in wideband fading channels: achievable bit rates and optimal bandwidth

In the context of fading channels it is well established that, with a constrained transmit power, the bit rates achievable by signals that are not peaky vanish as the bandwidth grows without bound. Stepping back from the limit, we characterize the highest bit rate achievable by such non-peaky signals and the approximate bandwidth where that apex occurs. As it turns out, the gap between the highest rate achievable without peakedness and the infinite-bandwidth capacity (with unconstrained peakedness) is small for virtually all settings of interest to wireless communications. Thus, although strictly achieving capacity in wideband fading channels does require signal peakedness, bit rates not far from capacity can be achieved with conventional signaling formats that do not exhibit the serious practical drawbacks associated with peakedness. In addition, we show that the asymptotic decay of bit rate in the absence of peakedness usually takes hold at bandwidths so large that wideband fading models are called into question. Rather, ultrawideband models ought to be used.

Optimal Contracts, Adverse Selection, and Social Preferences: An Experiment

It has long been standard in agency theory to search for incentive-compatible mechanisms on the assumption that people care only about their own material wealth. However, this assumption is clearly refuted by numerous experiments, and we feel that it may be useful to consider nonpecuniary utility in mechanism design and contract theory. Accordingly, we devise an experiment to explore optimal contracts in an adverse-selection context. A principal proposes one of three contract menus, each of which offers a choice of two incentive-compatible contracts, to two agents whose types are unknown to the principal. The agents know the set of possible menus, and choose to either accept one of the two contracts offered in the proposed menu or to reject the menu altogether; a rejection by either agent leads to lower (and equal) reservation payoffs for all parties. While all three possible menus favor the principal, they do so to varying degrees. We observe numerous rejections of the more lopsided menus, and approach an equilibrium where one of the more equitable contract menus (which one depends on the reservation payoffs) is proposed and agents accept a contract, selecting actions according to their types. Behavior is largely consistent with all recent models of social preferences, strongly suggesting there is value in considering nonpecuniary utility in agency theory.

A theory of optimal random crackdowns

An incentives based theory of policing is developed which can explain the phenomenon of random “crackdowns,” i.e., intermittent periods of high interdiction/surveillance. For a variety of police objective functions, random crackdowns can be part of the optimal monitoring strategy. We demonstrate support for implications of the crackdown theory using traffic data gathered by the Belgian Police Department and use the model to estimate the deterrence effectof additional resources spent on speeding interdiction.

On optimal monetary and fiscal policy interactions in open economies

This paper studies monetary and fiscal policy interactions in a two country model, where taxes on firms sales are optimally chosen and the monetary policy is set cooperatively.It turns out that in a two country setting non-cooperative fiscal policy makers have an incentive to change taxes on sales depending on shocks realizations in order to reduce output production. Therefore whether the fiscal policy is set cooperatively or not matters for optimal monetary policy decisions. Indeed, as already shown in the literature, the cooperative monetary policy maker implements the flexible price allocation only when special conditions on the value of the distortions underlying the economy are met. However, if non-cooperative fiscal policy makers set the taxes on firms sales depending on shocks realizations, these conditions cannot be satisfied; conversely, when fiscal policy is cooperative, these conditions are fulfilled. We conclude that whether implementing the flexible price allocation is optimal or not depends on the fiscal policy regime.

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

Portfolio choice and the effects of liquidity

This paper shows how to introduce liquidity into the well known mean-variance framework of portfolio selection. Either by estimating mean-variance liquidity constrained frontiers or directly estimating optimal portfolios for alternative levels of risk aversion and preference for liquidity, we obtain strong effects of liquidity on optimal portfolio selection. In particular, portfolio performance, measured by the Sharpe ratio relative to the tangency portfolio, varies significantly with liquidity. Moreover, although mean-variance performance becomes clearly worse, the levels of liquidity onoptimal portfolios obtained when there is a positive preference for liquidity are much lower than on those optimal portfolios where investors show no sign of preference for liquidity.

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

When to carry eccentric products? Optimal retail assortment under consumer returns

To understand whether retailers should consider consumer returns when merchandising, we study howthe optimal assortment of a price-taking retailer is influenced by its return policy. The retailer selects itsassortment from an exogenous set of horizontally differentiated products. Consumers make purchase andkeep/return decisions in nested multinomial logit fashion. Our main finding is that the optimal assortmenthas a counterintuitive structure for relatively strict return policies: It is optimal to offer a mix of the mostpopular and most eccentric products when the refund amount is sufficiently low, which can be viewed asa form of risk sharing between the retailer and consumers. In contrast, if the refund is sufficiently high, orwhen returns are disallowed, optimal assortment is composed of only the most popular products (a commonfinding in the literature). We provide preliminary empirical evidence for one of the key drivers of our results:more eccentric products have higher probability of return conditional on purchase. In light of our analyticalfindings and managerial insights, we conclude that retailers should take their return policies into accountwhen merchandising.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

On optimal location with treshold requirements

The optimal location of services is one of the most important factors that affects service quality in terms of consumer access. On theother hand, services in general need to have a minimum catchment area so as to be efficient. In this paper a model is presented that locates the maximum number of services that can coexist in a given region without having losses, taking into account that they need a minimum catchment area to exist. The objective is to minimize average distance to the population. The formulation presented belongs to the class of discrete P--median--like models. A tabu heuristic method is presented to solve the problem. Finally, the model is applied to the location of pharmacies in a rural region of Spain.

Optimal regulation of a fully insured deposit banking system

We analyze risk sensitive incentive compatible deposit insurancein the presence of private information when the market value of depositinsurance can be determined using Merton's (1997) formula. We show that,under the assumption that transferring funds from taxpayers to financialinstitutions has a social cost, the optimal regulation combines differentlevels of capital requirements combined with decreasing premia on depositinsurance. On the other hand, it is never efficient to require the banksto hold riskless assets, so that narrow banking is not efficient. Finally,chartering banks is necessary in order to decrease the cost of asymmetricinformation.