Statistical arbitrage in jump-diffusion models with compound Poisson processes

We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via 'buy-and-hold until barrier' and 'short until barrier' strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.

Automated summary

The paper proves the existence of statistical arbitrage opportunities in jump-diffusion models of stock prices with finite moments in the jump-size distribution. It demonstrates that in order to achieve statistical arbitrage, the holding of the risky asset must decrease over time. Statistical arbitrage is shown through 'buy-and-hold until barrier' and 'short until barrier' strategies with both single and double barriers, highlighting the need for a good approximation of the physical probability measure and drift of the stochastic process for a given asset in order to exploit these opportunities.