2012/09/03 by Andreas Neuenkirch, Łukasz Szpruch, Neuenkirch, Andreas +1
Economics, Econometrics and Finance · #60H10 #65J15 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Monetary Policy and Economic Impact #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1209.0390
openalex publication_date 2012/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general result can be applied to many SDEs we encounter in mathematical finance and bio-mathematics. We will demonstrate flexibility of our approach by analysing classical examples of SDEs with sublinear coefficients (CIR, CEV models and Wright-Fisher diffusion) and also with superlinear coefficients (3/2-volatility, Ait-Sahalia model). Our goal is to justify an efficient Multi-Level Monte Carlo (MLMC) method for a rich family of SDEs, which relies on good strong convergence properties.