Article1993

DISCONTINUOUS ASSET PRICES AND NON‐ATTAINABLE CONTINGENT CLAIMS 1

58 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

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.

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References

1976Option pricing when underlying stock returns are discontinuous 1979Martingales and arbitrage in multiperiod securities markets 1981Martingales and stochastic integrals in the theory of continuous trading 1987Limit Theorems for Stochastic Processes 1972Stochastic Differential Equations 1991Option hedging for semimartingales 1992Martingale densities for general asset prices

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