## Martingale representation and non-attainable contingent claims.(English)Zbl 0790.90006

Kall, Peter (ed.), System modelling and optimization. Proceedings of the 15th IFIP conference, Zurich, Switzerland, September 2-6, 1991. Berlin: Springer-Verlag. Lect. Notes Control Inf. Sci. 180, 833-842 (1992).
This paper considers the problem of hedging against contingent claims in the case where the underlying risky asset $$\xi$$ is described by a Markov diffusion with jumps. In general there may be many equivalent martingale measures in this model. Furthermore, contingent claims may not be attainable, and the market may not be complete. However, using a martingale representation result, the local risk-minimizing trading strategy is explicitly constructed. This in turn provides a new motivation for the concept of the minimal martingale measure.
For the entire collection see [Zbl 0778.00028].

### MSC:

 91B28 Finance etc. (MSC2000) 91B62 Economic growth models 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 91B24 Microeconomic theory (price theory and economic markets)