An expansion in the model space in the context of utility maximization

In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.     

Public goods with congestion

I consider the problem of the efficient provision of a congested (limited capacity) public good in a setting with asymmetric information. I show, in particular, that when the capacity of the good is limited, in a wide class of economies it is possible to construct an incentive compatible mechanism that always produces the good at the efficient level, balances the budget and satisfies voluntary participation constraints. This result is in contrast with the corresponding impossibility result for pure public goods due to Mailath and Postlewaite (Rev. Econ. Stud. 57 (1990) 351-359) and Rob (J. Econ. Theory 47 (1989) 307-333).     

Measuring competition in spatial retail

We propose and estimate a spatially aggregated discrete-choice model with overlapping consumer choice sets and demographic-driven heterogeneity that varies by chain. Our approach avoids the need to define markets ex ante and captures rich substitution patterns, even in the absence of price data. An application to the US grocery industry illustrates the importance of location, format, and the spatial distribution of consumers in shaping the competitive environment. Contrary to conventional wisdom, we find substantial cross-format competition between supercenters, clubs, and traditional grocers. Finally, we evaluate two representative mergers between supermarket chains to demonstrate how our estimates inform antitrust policy.     

Inefficient ex-post equilibria in efficient auctions

Summary. I consider a single-object English auction with two asymmetric bidders and show that it has a continuum of inefficient undominated ex-post equilibria. The result extends for the generalized VCG mechanism, Dasgupta-Maskin auction and, generally, for every auction that has an efficient ex-post equilibrium. Received: November 5, 2001; revised version: June 10, 2002 RID="*" ID="*"I am grateful to Vijay Krishna, Sergei Izmalkov and anonymous referee for many important comments.     

Sensitivity analysis of the utility maximisation problem with respect to model perturbations

Finance and Stochastics - We consider the expected utility maximisation problem and its response to small changes in the market price of risk in a continuous semimartingale setting. Assuming that...     

On efficiency of the English auction

We study efficiency properties of the irrevocable exit English auction in a setting with interdependent values. Maskin (1992) [1] shows that the pairwise single-crossing condition is sufficient for efficiency of the English auction with two bidders and suggests that it is also a necessary condition. This paper clarifies and extends Maskin?s results to the case of N bidders. We introduce the generalized single-crossing condition—a fairly intuitive extension of the pairwise single-crossing condition—and prove that it is essentially a necessary and sufficient condition for the existence of an efficient equilibrium of the N-bidder English auction.     

UTILITY MAXIMIZATION IN A LARGE MARKET

We study the problem of expected utility maximization in a large market, i.e., a market with countably many traded assets. Assuming that agents have von Neumann–Morgenstern preferences with stochastic utility function and that consumption occurs according to a stochastic clock, we obtain the “usual” conclusions of the utility maximization theory. We also give a characterization of the value function in a large market in terms of a sequence of value functions in finite‐dimensional models.     

OPTIMAL INVESTMENT WITH INTERMEDIATE CONSUMPTION AND RANDOM ENDOWMENT

We consider an optimal investment problem with intermediate consumption and random endowment, in an incomplete semimartingale model of the financial market. We establish the key assertions of the utility maximization theory, assuming that both primal and dual value functions are finite in the interiors of their domains and that the random endowment at maturity can be dominated by the terminal value of a self‐financing wealth process. In order to facilitate the verification of these conditions, we present alternative, but equivalent conditions, under which the conclusions of the theory hold.