We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

We consider a full equilibrium model in continuous time comprising a finite number of agents and tradable securities.We show that, if the agents' endowments are spanned by the securities and if the agents have entropic utilities, an equilibrium exists and the agents' optimal trading strategies...

We show how Adjoint Algorithmic Differentiation (AAD) can be used to calculate price sensitivities in regression-based Monte Carlo methods reliably and orders of magnitude faster than with standard finite-difference approaches. We present the AAD version of the celebrated least-square algorithms...