We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and of a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information. We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy.

We prove the existence of equilibrium in a continuous-time finance model; our results include the case of dynamically incomplete markets as well as dynamically complete markets. In addition, we derive explicitly the stochastic process describing securities prices. The price process depends on the risk-aversion characteristics of the utility function, as well as on the presence of additional sources of wealth (including endowments and other securities). With a single stock, zero endowment in the terminal period, and Constant Relative Risk Aversion (CRRA) utility, the price process is geometric Brownian motion; in essentially any other situation, the price process is not a geometric Brownian motion. Copyright Springer-Verlag Berlin/Heidelberg 2005Continuous time GEI, Asset pricing, Market clearing.,

We develop a method of assigning unique prices to derivative securities, including options, in the continuous-time finance model developed in Raimondo (2001). In contrast with the martingale method of valuing options, which cannot distinguish among infinitely many possible option pricing processes for a given underlying securities price process when markets are dynamically incomplete, our option prices are uniquely determined in equilibrium in closed form as a function of the underlying economic data. Copyright Springer-Verlag Berlin/Heidelberg 2005Option pricing, General equilibrium, Dynamically incomplete markets.,

We prove that if an operator A is a finite sum of finite products of Toeplitz operators on the Bergman space of the unit ball B n , then A is compact if and only if its Berezin transform vanishes at the boundary. For n = 1 the result was obtained by Axler and Zheng in 1997.

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