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INFINITE HORIZON INCOMPLETE MARKETS WITH A CONTINUUM OF STATES
Author(s) -
Araujo Aloisio,
Monteiro Paulo K.,
P´ascoa M´rio Rui
Publication year - 1996
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1996.tb00074.x
Subject(s) - countable set , mathematical economics , bounded function , incomplete markets , mathematics , economics , honor , node (physics) , lemma (botany) , discrete mathematics , computer science , neoclassical economics , mathematical analysis , physics , ecology , poaceae , quantum mechanics , biology , operating system
In this paper we address existence of equilibria in an incomplete markets economy with countably many periods and a continuum of states at each node of the infinite tree. We consider two models: one where agents have to honor their commitments and another where default is allowed. In both models, marginal utility of income, at each node, is shown to be bounded, and we prove existence by taking finite‐dimensional approximations and applying Fatou's lemma sequentially.