Strong order one convergence of the projected Euler–Maruyama method for the Wright–Fisher model

Abstract

The Wright–Fisher model is a useful SDE model, and it has many applications in finance and biology. However, it does not have an analytical solution currently. In this paper, we introduce a boundary preserving numerical method, called the projected EM method, to simulate it. We first use the projected EM method for the Lamperti transformed Wright–Fisher model. Then generated numerical solutions are transformed to derive the numerical approximations for the original Wright–Fisher model. We will use a new numerical analysis method to prove uniformly bounded inverse moments of the projected EM numerical solution, and then study the strong convergence of the projected EM method. Compared to existing explicit EM methods for the Wright–Fisher model, the projected EM method is strongly convergent with order one in more general $L^p$-norm and for more parameter settings.