DISCONTINUOUS ASSET PRICES AND NON‐ATTAINABLE CONTINGENT CLAIMS¹

Abstract

The price of a risky asset § is described by a Markov diffusion with jumps. In general there may be many equivalent martingale measures. Contingent claims which depend on the price of § at some time T may not be attainable, and the market may not be complete. However, using a martingale representation result, the local risk‐minimizing strategy is explicitly constructed. This in turn provides a new motivation for the concept of the minimal martingale measure.