A Microeconomic Approach to Diffusion Models For Stock Prices

Abstract

This paper studies a class of diffusion models for stock prices derived by a microeconomic approach. We consider discrete‐time processes resulting from a market equilibrium and then apply an invariance principle to obtain a continuous‐time model. the resulting process is an Ornstein‐Uhlenbeck process in a random environment, and we analyze its qualitative behavior. In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case.

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