Bond Market Completeness Under Stochastic Strings with Distribution-Valued Strategies

We study bond market completeness under infinite-dimensional models and show that, with stochastic string models, the market is complete if we consider strategies as generalized functions. We also obtain completeness for infinite-dimensional HJM models within the stochastic string framework. This result is not at odds with the incompleteness obtained in Barski et al. (2011). For a wide class of options, we obtain a new result, referred to as T-forward hedging, and we show that T-forward and delta hedging are equivalent in the Gauss-Markov case. As an application, we obtain a closed-form expression for the price of some compound options. Finally, we prove that in the stochastic string HJM case the martingale measure is unique, whereas in the general stochastic string case uniqueness is equivalent to a condition on the form of specific market risk premia