摘要翻译:
我们对具有非Lipschitz系数的一维SDEs的强近似感兴趣,它取一个域中的值。在一组一般假设下,我们导出了一个隐式格式,该格式保持了SDEs的区域,并且以速率1强收敛。此外,我们还证明了这一普遍结果可以应用于我们在数学金融和生物数学中遇到的许多SDE。我们将通过分析具有次线性系数(CIR、CEV模型和Wright-Fisher扩散)和具有超线性系数(3/2-波动率、Ait-Sahalia模型)的SDEs的经典例子来证明我们方法的灵活性。我们的目标是证明一个高效的多级蒙特卡罗(MLMC)方法对一个丰富的SDEs族是合理的,它依赖于良好的强收敛性。
---
英文标题:
《First order strong approximations of scalar SDEs with values in a domain》
---
作者:
Andreas Neuenkirch and Lukasz Szpruch
---
最新提交年份:
2012
---
分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Computational Finance 计算金融学
分类描述:Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法,包括蒙特卡罗,偏微分方程,格子和其他数值方法,并应用于金融建模
--
一级分类:Mathematics 数学
二级分类:Numerical Analysis 数值分析
分类描述:Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法,科学计算
--
---
英文摘要:
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.
---
PDF链接:
https://arxiv.org/pdf/1209.0390