Strong Convergence of the Truncated Euler–Maruyama Method for Nonlinear Stochastic Differential Equations with Jumps

The truncated Euler–Maruyama (EM) method for stochastic differential equations with Poisson jumps (SDEwPJs) has been proposed by Deng et al. in 2019. Although the finite-time Lr-convergence theory has been established, the strong convergence theory remains absent. In this paper, the strong convergence refers to the use of an L2 measure and places the supremum over time inside the expectation operation. Our version can be used to justify the method within Monte Carlo simulations that compute the expected payoff of financial products. Noting that the conditions imposed are too strict, this paper presents an existence and uniqueness theorem for SDEwPJs under general conditions and proves the convergence of the truncated EM method for these equations. Finally, two examples are considered to illustrate the application of the truncated EM method in option price calculation.