In this paper we discuss the existence of an optimal portfolio for every investor in a two-period Arrow-Debreu economy in which risky assets are contingent claims on aggregate consumption. Since we derive an optimal portfolio for every investor, the pricing kernel is endogenously determined. Hence the sufficient conditions for the existence of optimal portfolios given in this paper do not invol...

The Arrow-Debreu model of a perfectly competitive economy is based on the crucial assumption of complete markets, that is, the assumption that there exists a market (i.e. a price) for each good, for each location, for each future date and for each possible state of nature. The presence of a complete set of forward markets for future contingent delivery eliminates uncertainty since it allows com...

The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-v...

The Arrow-Debreu model of competitive markets has proven to be a remarkably rich and °exible foundation for studying an array of important economic problems, ranging from social security reform to the determinants of long-run growth. Central to the study of such questions are many of the extensions and modi ̄cations of the classic Arrow-Debreu framework that have been advanced over the last 40 y...

When reassessing the role of Debreu’s axiomatic method in economics, one has to explain both its success and unpopularity; one has to explain the “bright shadow” Debreu cast on the discipline: sheltering, threatening, and difficult to pin down. Debreu himself did not expect to have such an influence. Before he received the Bank of Sweden Prize in 1983 he had never openly engaged with the method...