Abstract.
The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trading strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique.
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Björk, T., Di Masi, G., Kabanov, Y. et al. Towards a general theory of bond markets . Finance Stochast 1, 141–174 (1997). https://doi.org/10.1007/s007800050020
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DOI: https://doi.org/10.1007/s007800050020