Functional Itô calculus†

We extend some results of the Itô calculus to functionals of the current path of a process to reflect the fact that often the impact of randomness is cumulative and depends on the history of the process, not merely on its current value. We express the differential of the functional in terms of adequately defined partial derivatives to obtain an Itô formula. We develop an extension of the Feynman-Kac formula to the functional case and an explicit expression of the integrand in the Martingale Representation Theorem. We establish that under certain conditions, even path dependent options prices satisfy a partial differential equation in a local sense. We exploit this fact to find an expression of the price difference between two models and compute variational derivatives with respect to the volatility surface.     

The political economy of pricing and capacity decisions for congestible local public goods in a federal state

This paper studies the political economy of pricing and investment for excludable and congestible public goods in a federal state. Although the model applies to many local congestible public facilities (such as libraries, museums and public swimming facilities), our main motivation is the problem of providing and pricing road infrastructure in federal states. The two-region model we develop allows for spill-overs between regions, it takes into account congestion, and it captures demand heterogeneity both between and within regions. Regional decisions are taken by majority voting; federal decisions are taken by a minimum winning coalition in a legislature of regionally elected representatives. We have the following results. First, when users form the majority in at least one region, decentralized decision making performs certainly better than centralized decision making if spill-overs are not too large. Centralized decisions may yield higher welfare than decentralization only if users have a large majority and the infrastructure in a given region is intensively used by both local and outside users. Second, if non-users form a majority in both regions, centralized decision making and decentralized decision making yield the same socially undesirable outcome, with prices that are much too high. Third, the performance of decentralized supply is strongly enhanced by local self-financing rules; this prevents potential exploitation of users within regions.     

WTO Disciplines on Domestic Support and Market Access in Agri‐Food Supply Chains

Multilateral negotiations on agriculture in the WTO are making very little progress as developed economies are reluctant to bind trade‐distorting domestic support and import tariffs at levels acceptable to developing countries. This paper presents the basic Bagwell–Staiger framework as it relates to agricultural trade negotiations. In its basic version, market access commitments are sufficient to achieve efficient trade agreements. We show that vertical linkages between agricultural goods and processed food commodities may prevent countries to reach an efficient trade agreement. We argue that the features of agricultural supply chains hinder the argument that total discretion over domestic policies is appropriate. Les négociations multilatérales de l'OMC sur l'agriculture progressent très lentement étant donné que les pays développés hésitent à maintenir un soutien interne qui fausse les échanges et des barrières tarifaires à des niveaux acceptables pour les pays en développement. Le présent article traite du modèle Bagwell–Staiger dans le contexte des négociations sur le commerce des produits agricoles. Dans sa version de base, les engagements quant à l'accès au marché sont suffisants pour permettre des échanges commerciaux efficaces. Nous montrons que les liens verticaux entre les produits agricoles et les produits alimentaires transformés peuvent empêcher les pays d'atteindre un accord commercial efficace. Nous soutenons que les caractéristiques des chaînes d'approvisionnement agricole entravent l'argument voulant que l'entière discrétion quant aux politiques intérieures soit appropriée.     

Analytical methods for planning educational facilities in an era of declining enrollments

With declining enrollments, metropolitan school districts are faced with problems of property disposition. A school facilities planning and management model utilizing a linear programming approach enables assessment of alternative uses for school facilities. The objective in this study is to minimize expenditures subject to constraints which include a limit to distance traveled, racial ethnic quotas, and overhead costs, such as transportation, maintenance and energy. An economic post-optimal cost sensitivity analysis of the proposed options is presented and also a comparison of this approach to school management with others found in the literature.     

Is Wheat a Homogeneous Product?

A hedonic approach is used to test for two kinds of product differentiation for wheat. It is shown that wheat is differentiated by end use and by country of origin. This simply recognizes the fact that buyers purchasing wheat for different purposes put different weights on quality criteria and that country-specific factors such as weather as well as grading and inspection systems matter. The results suggest that between 1980 and 1988, wheat protein content had a significant influence on price. This influence varies over time and across wheat categories.     

CONSUMPTION AND PORTFOLIO POLICIES WITH INCOMPLETE MARKETS AND SHORT-SALE CONSTRAINTS IN THE FINITE-DIMENSIONAL CASE: SOME REMARKS

This paper extends He and Pearson's (1991) martingale approach to the study of optimal intertemporal consumption and portfolio policies with incomplete markets and short-sale constraints to a framework in which no assumptions are made on the price process for the securities. We show how both their characterization of the budget-feasible set and duality result can be extended to account for an unbounded set II of Arrow-Debreu state prices compatible with the arbitrage-free assumption. We also supply a (fairly general) sufficient condition for II to be bounded, as required in their setting.