Abstract:

In this talk we discuss mathematical modelling of energy futures and briefly discuss some modelling decissions. Then we turn our attention to finite dimensional approximation of these models. From an economical perspective one should reject any model which allows for arbitrage. For this reason we deal with the question of finding an approximation of arbitrage-free finite dimensional models to a given one. The main problem is that finite-dimensionality enforces an invariance condition and the no-arbitrage condition enforces that a certain SPDE is solved under an equivalent measure. These together implies that the approximation models must be realised via so-called finite dimensional realisations of some SPDE. The problem is to ensure that the amount of these finite dimensional realisation models is rich enough to achieve an approximation to a given potentially infinite-dimensional model.