Arbitrage and equilibrium with portfolio constraints. (English) Zbl 1232.91615
Summary: We consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent’s portfolio choice is restricted to a closed, convex set containing zero, as in [P. Siconolfi, “Equilibrium with asymmetric constraints on portfolio holdings and incomplete financial markets”, in: Nonlinear dynamics in economics and social sciences. Bologna: Societa Pitagora, 271-292 (1989)]. Using an approach that dates back to D. Cass [“Competitive equilibrium with incomplete financial markets”, CARESS working paper, University of Pennsylvania (1984); J. Math. Econ. 42, No. 4–5, 384–405 (2006; Zbl 1141.91425)] in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduces that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent’s portfolio set. This latter result extends previous work by V. F. Martins-da-Rocha and L. Triki [“Equilibria in exchange economies with financial constraints: beyond the Cass trick”, working paper, Univ. Paris 1 (2005)].
MSC:
| 91G10 | Portfolio theory |
Keywords:
stochastic financial exchange economies; incomplete markets; financial equilibrium; constrained portfolios; multiperiod models; arbitrage-free asset pricesCitations:
Zbl 1141.91425References:
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