DISCONTINUOUS ASSET PRICES AND NON‐ATTAINABLE CONTINGENT CLAIMS1

David B. Colwell and Robert J. Elliott

Mathematical Finance, 1993, vol. 3, issue 3, 295-308

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.

Date: 1993
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