Conic Trading in Markovian Steady State

Abstract

Trading strategies are valued using non-linear conditional expectations with respect to non-additive probabilities in a discrete time Markovian context. Non-additive probabilities attain conservatism by exaggerating upwards tail loss events and exaggerating downwards tail gain events. Steady state fixed points for value and policy are obtained. It turns out to be critical that the valuation is conducted by an expectation with respect to a non-additive probability for with a classical conditional expectation operator both the value and policy iterations embedded in the associated Markov decision process fail. Illustrations are provided for Markovian systems in one, two and five dimensions. Trading positions are seen to balance prediction rewards against the demands for hedging value functions.