5. CONCLUSIONS
In this paper, we derive a new partial integro-differential inequality (PIDI) for shout options pricing on the assumption that the price of the underlying asset follows the jump-diffusion model and construct the mathematical model by combining specific features and terminal conditions. Another innovation is that this paper proposes a new competitive algorithm. Numerical experiments confirm the convergence in pricing shout options and shows that the algorithm proposed in this paper is superior to the traditional algorithm in the case of geometric Brownian motion and jump diffusion model, respectively.