Dynamic Consumption-Portfolio Choice and Asset Pricing with Non-Price-Taking Agents (Revised: 7-95)
This paper develops a continuous-time pure exchange model to theoretically study the dynamic consumption-portfolio problem of an agent who acts as a non-price-taker, and to analyze the implications of his behavior on the security prices and their dynamics. The non-price-taking behavior is modeled by allowing the non-price-taker’s consumption stream to affect Arrow-Debreu prices. This allows us to employ martingale methods in a natural way, making the analysis highly tractable. We define non-price-taking equilibrium in an economy of N price-takers and one non-price-taker, and show the existence and uniqueness of this equilibrium under common assumptions about the agents’ utility functions and dividend streams. Solving for the equilibrium consumption allocations reveals the existence of another driving factor apart from the aggregate consumption stream, the endowment stream of the non-price-taker, which leads to modified formulae for the interest rate and the consumption CAPM. We characterize the equilibrium consumption-portfolio allocations, and the Arrow-Debreu and security prices and their dynamics, i.e., the interest rate, market prices of risk, asset price volatility and risk premium. A variety of comparisons of equilibria between a price-taking and a non-price-taking economy are carried out, in some cases for general utility functions and in some cases for CARA utility of all agents. Intuition for the results is offered.
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