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<p>This paper investigates positivity-preserving numerical approximations for financial stochastic differential equations (SDEs) with highly nonlinear coefficients. We propose a truncated Euler-Maruyama (EM) scheme and establish its optimal strong convergence rates in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p(\varOmega ; \mathbb {R})\)</EquationSource> </InlineEquation> sense under appropriate regularity and integrability conditions, where <i>p</i> lies within a constrained parameter range. To demonstrate the versatility of our method, we apply the truncated scheme to two classes of financial SDEs: (i) models with highly nonlinear coefficients (e.g., the 3/2 and Aït-Sahalia models), which are approximated directly, and (ii) models with sublinear coefficients (e.g., the CIR model), handled via an indirect approach. Numerical experiments are provided to verify the effectiveness of our theoretical results.</p>

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Positivity-preserving approximations of financial SDEs with highly nonlinear coefficients: truncated Euler-Maruyama

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Shounian Deng,
  • Chen Fei,
  • Weiyin Fei

摘要

This paper investigates positivity-preserving numerical approximations for financial stochastic differential equations (SDEs) with highly nonlinear coefficients. We propose a truncated Euler-Maruyama (EM) scheme and establish its optimal strong convergence rates in the \(L^p(\varOmega ; \mathbb {R})\) sense under appropriate regularity and integrability conditions, where p lies within a constrained parameter range. To demonstrate the versatility of our method, we apply the truncated scheme to two classes of financial SDEs: (i) models with highly nonlinear coefficients (e.g., the 3/2 and Aït-Sahalia models), which are approximated directly, and (ii) models with sublinear coefficients (e.g., the CIR model), handled via an indirect approach. Numerical experiments are provided to verify the effectiveness of our theoretical results.