On martingale measures when asset returns have unpredictable jumps
The paper studies incompleteness in financial markets induced by discontinuities in asset returns. The uncertainty is present not only in the timing of the jump but in the jump size as well. It is shown that, differently from the pure diffusion case or the case of predictable jump sizes, contingent claims cannot be either hedged completely or fairly priced by arbitrage. However, the authors identify a family of martingale measures that arise from arbitrage considerations. Each of these measures is a price functional in some auxiliary market, although, even in the markets so augmented, full hedging is still impossible. Therefore, the martingale measures only supply a bound on the price of the claim.
scientific article; zbMATH DE number 1046568