The martingale theory of price bubbles defines an asset bubble to exist when the asset's price process is a strict local martingale, that is, a local martingale that is not a martingale. Using this definition of a price bubble, for continuous semimartingales, we characterize the conditions under...

We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization...

We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures privce curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a...