The Completeness and Incompleteness of Financial Markets in Economies Driven by Diffusion Processes

摘要

We investigate sufficient conditions for the completeness and incompleteness of financial markets with multiple goods and heterogeneous agents in continuous-time economies driven by diffusion processes. It is demonstrated that, under certain conditions, two types of utility functions lead to the incompleteness of markets, while the invertibility of the Jacobian matrix of dividend rates' volatility in units of the numeraire good gives rise to the completeness of markets. In particular, it is shown that if a type of special utility functions is adopted, then the change of numeraire good leads to the conversion of completeness of markets.