Positivity-preserving truncated Euler and Milstein methods for financial SDEs with super-linear coefficients
<|reference_start|>Positivity-preserving truncated Euler and Milstein methods for financial SDEs with super-linear coefficients: In this paper, we propose two variants of the positivity-preserving schemes, namely the truncated Euler-Maruyama (EM) method and the truncated Milstein scheme, applied to stochastic differential equations (SDEs) with positive solutions and super-linear coefficients. Under some regularity and integrability assumptions we derive the optimal strong convergence rates of the two schemes. Moreover, we demonstrate flexibility of our approaches by applying the truncated methods to approximate SDEs with super-linear coefficients (3/2 and Ai{\i}t-Sahalia models) directly and also with sub-linear coefficients (CIR model) indirectly. Numerical experiments are provided to verify the effectiveness of the theoretical results.<|reference_end|>
@article{deng2024positivity-preserving,
    title={Positivity-preserving truncated Euler and Milstein methods for financial
  SDEs with super-linear coefficients},
    author={Shounian Deng and Chen Fei and Weiyin Fei and Xuerong Mao},
    journal={arXiv preprint arXiv:2410.05614},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.05614},
    primaryClass={math.NA cs.NA}
}