Robust statistical arbitrage

Statistical Arbitrage Opportunity (SAO) originally introduced by Bondarenko(2003) is a zero-cost trading strategy for which (i) the expected payoff is positive, and (ii) the conditional expected payoff in each final state of the economy is nonnegative. Unlike pure arbitrage strategies, SAOs are not completely risk-free, but the notion allows to profit on average, given the outcome of a specific σ-algebra G. Previous work by L¨utkebohmert and Sester (2019) has provided mathematical investigation of SAO when there is ambiguity about the underlying time-discrete financial model. They proposed a linear programming approach that worked in low dimensions but suffered from the curse of dimensionality. In our work, we propose a novel neural network approach that allows flexible trading numbers per period and multi-asset trading. We also consider a more realistic scheme to introduce uncertainty to our strategy. We estimate the implied probability measure P from historical data and optimize with respect to a prior set of physical measures obtained by introducing some distortion to P. We prove a theoretical guarantee for the approach that solves the conditional superhedging problem and we provide numerical results.Bachelor of Science in Mathematical Science