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DISCONTINUOUS ASSET PRICES AND NON‐ATTAINABLE CONTINGENT CLAIMS 1
Author(s) -
Colwell David B.,
Elliott Robert J.
Publication year - 1993
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1993.tb00046.x
Subject(s) - martingale (probability theory) , local martingale , martingale pricing , economics , econometrics , markov chain , mathematical economics , markov process , risk neutral measure , doob's martingale inequality , asset (computer security) , mathematics , computer science , statistics , computer security
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.