We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.
De Donno, M., M., P., A theory of stochastic integration for bond markets, <<THE ANNALS OF APPLIED PROBABILITY>>, 2005; 15 (4): 2773-2791. [doi:10.1214/105051605000000548] [http://hdl.handle.net/10807/168913]
A theory of stochastic integration for bond markets
De Donno, Marzia;
2005
Abstract
We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.
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