Incomplete financial markets and jumps in asset prices

Abstract

For incomplete financial markets, jumps in both prices and consumption can be unavoidable. We consider pure-exchange economies with infinite horizon, discrete time, uncertainty with a continuum of possible shocks at every date. The evolution of shocks follows a Markov process, and fundamentals depend continuously on shocks. It is shown that: (1) equilibria exist; (2) for effectively complete financial markets, asset prices depend continuously on shocks; and (3) for incomplete financial markets, there is an open set of economies $${\fancyscript{U}}$$ such that for every equilibrium of every economy in $${\fancyscript{U}}$$ , asset prices at every date depend discontinuously on the shock at that date.