Publication

Endogenous Completeness of Diffusion Driven Equilibrium Markets

2009
Working Papers

Abstract

We study the existence of equilibria with endogenously complete mar- kets in a continuous-time, heterogenous agents economy driven by a multi- dimensional diﬀusion process. Our main results show that if prices are real analytic as functions of time and the state variables of the model then a suﬃ- cient condition for market completeness is that the volatility of dividends be nondegenerate. In contrast to previous research, our formulation does not require that securities pay terminal dividends and thus allows for both ﬁnite or inﬁnite horizon economies. We illustrate our results by providing easily applicable conditions for market completeness in two benchmark cases: that where the state variables are given by a vector autoregressive process and that where they are given by a vector of autonomous diﬀusion processes. We also provide counterexamples which show that real analyticity cannot be dispensed with if one is to deduce dynamic market completeness from the structure of dividends.

Official source

https://infoscience.epfl.ch/entities/publication/aa99ead7-636c-4f1a-9f9e-4aa1d418fd19

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2009
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/aa99ead7-636c-4f1a-9f9e-4aa1d418fd19

About this result

Related concepts (32)

Autoregressive model

In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).

Vector autoregression

Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series. VAR models are often used in economics and the natural sciences. Like the autoregressive model, each variable has an equation modelling its evolution over time.

Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about converges to the function in some neighborhood for every in its domain.