We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We...

We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk...

We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently with other studies, we find that the presence of linear...

We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance, which means that the dynamics of the economy should not...

In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge...