# Generalized statistical arbitrage concepts and related gain strategies

## TL;DR

This paper introduces a broad framework for statistical arbitrage that encompasses classical and new strategies, characterizes their no-arbitrage conditions, and demonstrates their effectiveness through simulations and market data.

## Contribution

It generalizes the concept of statistical arbitrage, including static and semi-static strategies, and constructs practical profitable strategies based on various information systems.

## Key findings

- Generalized strategies can yield positive average gains under certain scenarios.
- Constructed strategies perform well on simulated and real market data.
- The framework includes classical arbitrage as a special case.

## Abstract

Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via an information system given by a $\sigma$-algebra and so this notion contains classical arbitrage as a special case. It also covers the notion of statistical arbitrage introduced in Bondarenko (2003). Relaxing these notions further we introduce generalized profitable strategies which include also static or semi-static strategies. Under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios. In the first part of the paper we characterize these generalized statistical no-arbitrage notions. In the second part of the paper we construct several profitable generalized strategies with respect to various choices of the information system. In particular, we consider several forms of embedded binomial strategies and follow-the-trend strategies as well as partition-type strategies. We study and compare their behaviour on simulated data. Additionally, we find good performance on market data of these simple strategies which makes them profitable candidates for real applications.