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' strategy, where the investor sells the risky asset when it hits a deterministic boundary. 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