Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Satisfaction in choice as a function of the number of alternatives: When "goods satiate" but "bads escalate"

Whereas people are typically thought to be better off with more choices, studiesshow that they often prefer to choose from small as opposed to large sets of alternatives.We propose that satisfaction from choice is an inverted U-shaped function of thenumber of alternatives. This proposition is derived theoretically by considering thebenefits and costs of different numbers of alternatives and is supported by fourexperimental studies. We also manipulate the perceptual costs of information processingand demonstrate how this affects the resulting satisfaction function. We furtherindicate that satisfaction when choosing from a given set is diminished if people aremade aware of the existence of other choice sets. The role of individual differences insatisfaction from choice is documented by noting effects due to gender and culture. Weconclude by emphasizing the need to have an explicit rationale for knowing how muchchoice is enough.

Optimal second-degree price discrimination and arbitrage: On the role of asymetric information among buyers

The traditional theory of monopolistic screening tackles individualself-selection but does not address the possibility that buyers couldform a coalition to coordinate their purchases and to reallocate thegoods. In this paper, we design the optimal sale mechanism which takesinto account both individual and coalition incentive compatibilityfocusing on the role of asymmetric information among buyers. We showthat when a coalition of buyers is formed under asymmetric information,the monopolist can do as well as when there is no coalition. Although inthe optimal sale mechanism marginal rates of substitution are notequalized across buyers (hence there exists room for arbitrage), theyfail to realize the gains from arbitrage because of the transaction costsin coalition formation generated by asymmetric information.

New evidence on inflation persistence and price stickiness in the Euro area: Implications for macro modelling

This paper evaluates new evidence on price setting practices and inflation persistence in the euro area with respect to its implications for macro modelling. It argues that several of the most commonly used assumptions in micro-founded macro models are seriously challenged by the new findings.

Cost efficiency in primary care contracting: A stochastic frontier cost function approach

The principal aim of this paper is to estimate a stochastic frontier costfunction and an inefficiency effects model in the analysis of the primaryhealth care services purchased by the public authority and supplied by 180providers in 1996 in Catalonia. The evidence from our sample does not supportthe premise that contracting out has helped improve purchasing costefficiency in primary care. Inefficient purchasing cost was observed in thecomponent of this purchasing cost explicitly included in the contract betweenpurchaser and provider. There are no observable incentives for thecontracted-out primary health care teams to minimise prescription costs, whichare not explicitly included in the present contracting system.

Price regulation of plastic money: A critical assessment of Spanish rules

Recent decisions by the Spanish national competition authority (TDC) mandate paymentsystems to include only two costs when setting their domestic multilateral interchange fees(MIF): a fixed processing cost and a variable cost for the risk of fraud. This artificiallowering of MIFs will not lower consumer prices, because of uncompetitive retailing; but itwill however lead to higher cardholders fees and, likely, new prices for point of saleterminals, delaying the development of the immature Spanish card market. Also, to the extent that increased cardholders fees do not offset the fall in MIFs revenue, the task of issuing new cards will be underpaid relatively to the task of acquiring new merchants, causing an imbalance between the two sides of the networks. Moreover, the pricing scheme arising from the decisions will cause unbundling and underprovision of those services whose costs are excluded. Indeed, the payment guarantee and the free funding period will tend to be removed from the package of services currently provided, to be either provided by third parties, by issuers for a separate fee, or not provided at all, especially to smaller and medium-sized merchants. Transaction services will also suffer the consequences that the TDC precludes pricing them in variable terms.

A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

Minimum price variations, time priority and quotes dynamics

We analyze the impact of a minimum price variation (tick) and timepriority on the dynamics of quotes and the trading costs when competitionfor the order flow is dynamic. We find that convergence to competitiveoutcomes can take time and that the speed of convergence is influencedby the tick size, the priority rule and the characteristics of the orderarrival process. We show also that a zero minimum price variation is neveroptimal when competition for the order flow is dynamic. We compare thetrading outcomes with and without time priority. Time priority is shownto guarantee that uncompetitive spreads cannot be sustained over time.However it can sometimes result in higher trading costs. Empiricalimplications are proposed. In particular, we relate the size of thetrading costs to the frequency of new offers and the dynamics of theinside spread to the state of the book.

Pitfalls in the modeling of forward-looking price setting and investment decisions

The present paper makes progress in explaining the role of capital for inflation and output dynamics. We followWoodford (2003, Ch. 5) in assuming Calvo pricing combined with a convex capital adjustment cost at the firm level. Our main result is that capital accumulation affects inflation dynamics primarily through its impact on the marginal cost. This mechanism is much simpler than the one implied by the analysis in Woodford's text. The reason is that his analysis suffers from a conceptual mistake, as we show. The latter obscures the economic mechanism through which capital affects inflation and output dynamics in the Calvo model, as discussed in Woodford (2004).

Glutamine Stimulates Biosynthesis and Secretion of Insulin-like Growth Factor 2 (IGF2), an Autocrine Regulator of Beta Cell Mass and Function.

IGF2 is an autocrine ligand for the beta cell IGF1R receptor and GLP-1 increases the activity of this autocrine loop by enhancing IGF1R expression, a mechanism that mediates the trophic effects of GLP-1 on beta cell mass and function. Here, we investigated the regulation of IGF2 biosynthesis and secretion. We showed that glutamine rapidly and strongly induced IGF2 mRNA translation using reporter constructs transduced in MIN6 cells and primary islet cells. This was followed by rapid secretion of IGF2 via the regulated pathway, as revealed by the presence of mature IGF2 in insulin granule fractions and by inhibition of secretion by nimodipine and diazoxide. When maximally stimulated by glutamine, the amount of secreted IGF2 rapidly exceeded its initial intracellular pool and tolbutamide, and high K(+) increased IGF2 secretion only marginally. This indicates that the intracellular pool of IGF2 is small and that sustained secretion requires de novo synthesis. The stimulatory effect of glutamine necessitates its metabolism but not mTOR activation. Finally, exposure of insulinomas or beta cells to glutamine induced Akt phosphorylation, an effect that was dependent on IGF2 secretion, and reduced cytokine-induced apoptosis. Thus, glutamine controls the activity of the beta cell IGF2/IGF1R autocrine loop by increasing the biosynthesis and secretion of IGF2. This autocrine loop can thus integrate changes in feeding and metabolic state to adapt beta cell mass and function.

Price differentials in monetary unions: The role of fiscal shocks

We study the effect of regional expenditure and revenue shocks on price differentials for47 US states and 9 EU countries. We identify shocks using sign restrictions on the dynamicsof deficits and output and construct two estimates for structural price differentials dynamics which optimally weight the information contained in the data for all units. Fiscal shocks explain between 14 and 23 percent of the variability of price differentials both in the US and in the EU. On average, expansionary fiscal disturbances produce positive price differential responses while distortionary balance budget shocks produce negative price differential responses. In a number of units, price differential responses to expansionary fiscal shocks are negative. Spillovers and labor supply effects partially explain this pattern while geographical, political, and economic indicators do not.

Abnormal Lung Function and Risk for Heart Failure in the Elderly: The Health, Aging, and Body Composition Study

Background: Chronic obstructive pulmonary disease (COPD) has been associated with increased risk for heart failure (HF). The impact of subclinical abnormal spirometric findings on HF risk among older adults without history of COPD is not well elucidated. Methods: We evaluated 2125 participants (age 73.6±2.9 years; 50.5% men; 62.3% white; 45.6/9.4% past/current smokers; body mass index [BMI] 27.2±4.6 kg/m2) without prevalent COPD or HF who underwent baseline spirometry in the Health ABC Study. Abnormal lung function was defined either as forced vital capacity (FVC) below lower limit of normal (LLN) or forced expiratory volume in 1st sec (FEV1) to FVC ratio below LLN. Results: On follow-up (median, 9.4 years), 68 of 350 (19.4%) participants with abnormal lung function developed HF, as compared to 172 of 1775 (9.7%) participants with normal lung function (hazard ratio [HR], 2.31; 95% confidence interval [CI], 1.74 -3.06; P<.001). This increased risk persisted after adjusting for all other independent predictors of HF in the Health ABC Study, BMI, incident coronary events, and several inflammatory markers (HR, 1.82; 95% CI, 1.30 -2.54; P<.001), and remained constant over time. Baseline FVC and FEV1 had a linear association with HF risk (Figure). In adjusted models, HF risk increased by 21% (95% CI, 10 -36%) per 10% decrease in FVC and 18% (95% CI, 10 -28%) per 10% decrease in FEV1 (both P<.001); this association persisted among participants with normal lung function at baseline. Findings were consistent across sex, race, and smoking status. Conclusions: Subclinical abnormal spirometric findings are prevalent among older adults and are independently associated with risk for incident HF.

Identification of an agrin mutation that causes congenital myasthenia and affects synapse function.

We report the case of a congenital myasthenic syndrome due to a mutation in AGRN, the gene encoding agrin, an extracellular matrix molecule released by the nerve and critical for formation of the neuromuscular junction. Gene analysis identified a homozygous missense mutation, c.5125G>C, leading to the p.Gly1709Arg variant. The muscle-biopsy specimen showed a major disorganization of the neuromuscular junction, including changes in the nerve-terminal cytoskeleton and fragmentation of the synaptic gutters. Experiments performed in nonmuscle cells or in cultured C2C12 myotubes and using recombinant mini-agrin for the mutated and the wild-type forms showed that the mutated form did not impair the activation of MuSK or change the total number of induced acetylcholine receptor aggregates. A solid-phase assay using the dystrophin glycoprotein complex showed that the mutation did not affect the binding of agrin to alpha-dystroglycan. Injection of wild-type or mutated agrin into rat soleus muscle induced the formation of nonsynaptic acetylcholine receptor clusters, but the mutant protein specifically destabilized the endogenous neuromuscular junctions. Importantly, the changes observed in rat muscle injected with mutant agrin recapitulated the pre- and post-synaptic modifications observed in the patient. These results indicate that the mutation does not interfere with the ability of agrin to induce postsynaptic structures but that it dramatically perturbs the maintenance of the neuromuscular junction.