Maxentropic construction of risk neutral measures: discrete market models

Abstract

The maximum entropy principle provides a variational method to select a measure yielding pre-assigned mean values to a random variable. It can also be invoked to construct measures that render a stochastic process a martingale, thus providing a systematic way of constructing risk-neutral measures and thus closing a market. We carry out this programme for discrete market models. On the one hand these are amenable to numerical implementation and on the other, they provide a stepping stone for more general market models in continuous time.