Contributions to Intertemporal Models in Financial Economics

Abstract

Investors in financial markets face several restrictions apart from wealth constraints. The first attempt to understand these restrictions in a general competitive equilibrium framework can be traced back to Radner (1972). Here these restrictions are assumed to be given exogenously, as first modeled by Siconolfi (1986). Portfolio sets given by closed and convex sets containing zero are the most general form of portfolio restrictions. Such sets can accommodate most restrictions that investors actually face in financial markets, see Elsinger and Summer (2000). The traditional Arrow-Debreu general equilibrium models can then be extended to a more realistic setting. Following Angeloni and Cornet (2006), this extension of the Arrow-Debreu model in the multi-period setting with restricted participation is established. Once investors are assumed to face such portfolio restrictions, there is a need to differentiate individual arbitrage opportunities from those at the aggregate level. In the special case where the portfolio sets linear subspace (for example investors invest only through some mutual funds), this difference in the notion of arbitrage at the individual level and the aggregate level is characterized. Extending the 2-date result of Hens et al., we show that generically there will be some arbitrage opportunities that remain unexploited at the aggregate level. The existence of a general financial equilibrium, an equilibrium in all markets (commodities and financial assets) has been extensively studied in 2-date, multi-period and infinite horizon models. With such general portfolio constraints, using an approach that dates back to Cass 1984, we look for arbitrage-free asset prices at the aggregate level that are also equilibrium asset prices. For this approach, we present a condition on the space of income transfers which makes the existence result in this work very general and the previous results in this area turn out to be special cases.