In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with motivation and basis theory, we formally derive Bogoliubov inequality discuss itself. We proceed use determine magnetisation function, results derivation are interpreted graphically, physically, mathematically. give new interpretation self-consist...

We introduce a mean-field extension of the LIBOR market model (LMM) which preserves basic features original model. Among others, these are martingale property, directly implementable calibration and an economically reasonable parametrization classical LMM. At same time, (MF-LMM) is designed to reduce probability exploding scenarios, arising in particular market-consistent valuation long-term gu...