On incompleteness of bond markets with infinite number of random factors

The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market in the case of trading strategies is not complete. An explicit construction of a bounded contingent claim, which can not be replicated, is provided. Moreover, a new concept of generalized strategies is introduced and sufficient conditions for the market completeness with such strategies are given. An example of a complete model is provided.