AN EULER-POISSON SCHEME FOR LEVY DRIVEN STOCHASTIC DIFFERENTIAL EQUATIONS

作者：Ferreiro Castilla A^*; Kyprianou A E; Scheichl R

来源：Journal of Applied Probability, 2016, 53(1): 262-278.

DOI：10.1017/jpr.2015.23

• Levy process
• Euler scheme
• meromorphic Levy process
• stochastic differential equation

We describe an Euler scheme to approximate solutions of Levy driven stochastic differential equations (SDEs) where the grid points are given by the arrival times of a Poisson process and thus are random. This result extends the previous work of Ferreiro-Castilla et al. (2014). We provide a complete numerical analysis of the algorithm to approximate the terminal value of the SDE and prove that the mean-square error converges with rate O(n(-1/2)). The only requirement of the methodology is to have exact samples from the resolvent of the Levy process driving the SDE. Classical examples, such as stable processes, subclasses of spectrally one-sided Levy processes, and new families, such as meromorphic Levy processes (Kuznetsov et al. (2012), are examples for which our algorithm provides an interesting alternative to existing methods, due to its straightforward implementation and its robustness with respect to the jump structure of the driving Levy process.

• 出版日期2016-3