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.

Money doctors

We present a new model of money management, in which investors delegate portfolio management to professionals based not only on performance, but also on trust. Trust in the manager reduces an investor's perception of the riskiness of a given investment, and allows managers to charge higher fees to investors who trust them more. Money managers compete for investor funds by setting their fees, but because of trust the fees do not fall to costs. In the model, 1) managers consistently underperform the market net of fees but investors still prefer to delegate money management to taking risk on their own, 2) fees involve sharing of expected returns between managers and investors, with higher fees in riskier products, 3) managers pander to investors when investors exhibit biases in their beliefs, and do not correct misperceptions, and 4) despite long run benefits from better performance, the profits from pandering to trusting investors discourage managers from pursuing contrarian strategies relative to the case with no trust. We show how trust-mediated money management renders arbitrage less effective, and may help destabilize financial markets.

Bands width, credibility and exchange risk: Lessons from the EMS experience

This paper presents an analysis of the credibility of the EMScurrencies that covers the period before and after the increase in thebands of fluctuation. Our credibility indicator is based on the inferredprobabilities derived from the estimation of a Markov-switching model(Hamilton (1989)) applied to the expected rate of depreciation. Theresults show that, for most of the currencies, credibility has improved,at least transitorily, after the increase in the bands. However, for allcurrencies, the credibility measured by the indicator proposed in thispaper has been eroded recently even with the widened bands.

On the impact of leverage constraints on asset prices and trading volume

Researchers have used stylized facts on asset prices and trading volumein stock markets (in particular, the mean reversion of asset returnsand the correlations between trading volume, price changes and pricelevels) to support theories where agents are not rational expected utilitymaximizers. This paper shows that this empirical evidence is in factconsistent with a standard infite horizon perfect information expectedutility economy where some agents face leverage constraints similar tothose found in todays financial markets. In addition, and in sharpcontrast to the theories above, we explain some qualitative differencesthat are observed in the price-volume relation on stock and on futuresmarkets. We consider a continuous-time economy where agents maximize theintegral of their discounted utility from consumption under both budgetand leverage con-straints. Building on the work by Vila and Zariphopoulou(1997), we find a closed form solution, up to a negative constant, for theequilibrium prices and demands in the region of the state space where theconstraint is non-binding. We show that, at the equilibrium, stock holdingsvolatility as well as its ratio to stock price volatility are increasingfunctions of the stock price and interpret this finding in terms of theprice-volume relation.

The wage effect of an indexation clause: Evidence from Spanish manufacturing firms

An endogenous switching model of ex-ante wage changes under indexed and non-indexed settlements is estimated for the Spanish manufacturing sector using collective bargaining firm data for the 1984-1991 period. The likelihood of indexing the settlement is higher for nationwide unions than for other union groups within the works council and increases with the expected level of inflation. For wage change equations, a common structure for indexed and non-indexed settlements is strongly rejected, showing a source of nominal rigidity. For indexed contracts, the expected ex-ante total inflation coverage is nearly complete. It is also shown that workers pay a significant ex-ante wage change premium (differential) to obtain a cost of living allowance clause. However, the realised contingent compensation exceeds such a premium for all industries. Finally, important spillover effects in wage setting and the decision to index the settlement have been detected.

Bubbly collateral and economic activity

This paper develops a model of the bubbly economy and uses it to study the effects of bailoutpolicies. In the bubbly economy, weak enforcement institutions do not allow firms to pledge futurerevenues to their creditors. As a result, "fundamental" collateral is scarce and this impairs the intermediationprocess that transforms savings into capital. To overcome this shortage of "fundamental"collateral, the bubbly economy creates "bubbly" collateral. This additional collateral supports anintricate array of intra- and inter-generational transfers that allow savings to be transformed intocapital and bubbles. Swings in investor sentiment lead to fluctuations in the amount of bubblycollateral, giving rise to bubbly business cycles with very rich and complex dynamics.Bailout policies can affect these dynamics in a variety of ways. Expected bailouts provideadditional collateral and expand investment and the capital stock. Realized bailouts reduce thesupply of funds and contract investment and the capital stock. Thus, bailout policies tend to fosterinvestment and growth in normal times, but to depress investment and growth during crisis periods.We show how to design bailout policies that maximize various policy objectives.

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

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.

Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

Targeting fertility and female participation through the income tax

We evaluate the effect of a 2003 reform in the Spanish income tax on fertility and the employment of mothers with small children. The reform introduced a tax credit for working mothers with children under the age of three, while also increasing child deductions for all households with children. Theoretically, given the interplay of these two components, the expected effect of the reform is ambiguous on both outcomes. We find that the combined reforms significantly increased both fertility (by almost five percent) and the employment rate of mothers with children under three (by two percent). These effects were more pronounced among less-educated women. In addition, to disentangle the impact of the two reform components, we use an earlier reform that increased child deductions in 1999. We find that the child deductions affect mothers employment negatively, which implies that the 2003 tax credit would have increased employment even more (up to five percent) in the absence of the change in child deductions.

Generic entry into a regulated pharmaceutical market

The aim of this paper is to analyse empirically entry decisions by generic firms intomarkets with tough regulation. Generic drugs might be a key driver of competitionand cost containment in pharmaceutical markets. The dynamics of reforms ofpatents and pricing across drug markets in Spain are useful to identify the impact ofregulations on generic entry. Estimates from a count data model using a panel of 86active ingredients during the 1999 2005 period show that the drivers of genericentry in markets with price regulations are similar to less regulated markets: genericfirms entries are positively affected by the market size and time trend, and negativelyaffected by the number of incumbent laboratories and the number of substitutesactive ingredients. We also find that contrary to what policy makers expected, thesystem of reference pricing restrains considerably the generic entry. Short run brandname drug price reductions are obtained by governments at the cost of long runbenefits from fostering generic entry and post-patent competition into the markets.

Crime and punishment: Further results

I consider a general specification of criminals' objective functionand argue that, when the general non-expected utility theory issubstituted for the traditional expected utility theory, thehigh-fine-low-probability result (Becker, 1968) only holds underspecific and strong restrictions.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Testing the descriptive performance of the rank-dependent utility in the domain of health profiles

Expected utility theory (EUT) has been challenged as a descriptive theoryin many contexts. The medical decision analysis context is not an exception.Several researchers have suggested that rank dependent utility theory (RDUT)may accurately describe how people evaluate alternative medical treatments.Recent research in this domain has addressed a relevant feature of RDU models-probability weighting-but to date no direct test of this theoryhas been made. This paper provides a test of the main axiomatic differencebetween EUT and RDUT when health profiles are used as outcomes of riskytreatments. Overall, EU best described the data. However, evidence on theediting and cancellation operation hypothesized in Prospect Theory andCumulative Prospect Theory was apparent in our study. we found that RDUoutperformed EU in the presentation of the risky treatment pairs in whichthe common outcome was not obvious. The influence of framing effects onthe performance of RDU and their importance as a topic for future researchis discussed.

Strategic behavior and price discovery

The paper analyzes the effects of strategic behavior by an insider in a price discovery process, akin to an information tatonnement, in the presence of a competitive informed sector. Such processes are used in the preopening period of continuous trading systems in several exchanges. It is found that the insider manipulates the market using a contrarian strategy in order to neutralize the effect of the trades of competitive informed agents. Furthermore, consistently with the empirical evidence available, we find that information revelation accelerates close to the opening, that the market price does not converge to the fundamental value no matter how many rounds the tatonnement has, and that the expected trading volume displays a U-shaped pattern. We also find that a market with a larger competitive sector (smaller insider) has an improved informational efficiency and an increased trading volume. The insider provides a public good (a lower informativeness of the price) for the competitive informed sector.