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A theory of stochastic integration for bond markets. (English) Zbl 1121.60056

A theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter and a characterization of the class of integrands are presented. This stochastic integral generalizes the stochastic integral introduced by T. Björk, G. Di Masi, Y. Kabanov and W. Runggaldier [Finance Stoch. 1, No. 2, 141–174 (1997; Zbl 0889.90019)]. The stochastic integral defined by the authors is linear and is invariant with respect to a change by an equivalent probability measure, but it is not stable for small perturbations of the semimartingale and not linear with respect to the integrator. They apply their results to the problem of super-replication and utility maximization from terminal wealth in a bond market. The authors compare their theory with other approaches based on infinite-dimensional stochastic integration.

MSC:

60H05 Stochastic integrals
60G44 Martingales with continuous parameter
91B70 Stochastic models in economics

Citations:

Zbl 0889.90019
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References:

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