Complete markets with discontinuous security price

Abstract.

A parameterized family of financial market models is presented. These models have jumps intrinsic to the price processes yet have strict completeness, equivalent martingale measures, and no arbitrage. For each value of the parameter $\beta (-2\leq\beta <0)$ the model is just as rich as the standard model using white noise (Brownian motion) and a drift; moreover as $\beta$ increases to zero the model converges weakly to the standard model. A hedging result, analogous to the Karatzas-Ocone-Li theorem, is also presented.