Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The truncated EM scheme for multiple-delay SDEs with irregular coefficients and application to stochastic volatility model

Zhuoqi Liu, Zhaohang Wang, Siying Sun, Shuaibin Gao

Abstract

This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially Hölder continuous drifts and locally Hölder continuous diffusion coefficients. To handle with the superlinear terms in coefficients, the truncated Euler-Maruyama scheme is employed. Under the given conditions, the convergence rates at time $T$ in both $\mathcal{L}^{1}$ and $\mathcal{L}^{2}$ senses are shown by virtue of the Yamada-Watanabe approximation technique. Moreover, the convergence rates over a finite time interval $[0,T]$ are also obtained. Additionally, it should be noted that the convergence rates will not be affected by the number of delay variables. Finally, we perform the numerical experiments on the stochastic volatility model to verify the reliability of the theoretical results.

The truncated EM scheme for multiple-delay SDEs with irregular coefficients and application to stochastic volatility model

Abstract

This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially Hölder continuous drifts and locally Hölder continuous diffusion coefficients. To handle with the superlinear terms in coefficients, the truncated Euler-Maruyama scheme is employed. Under the given conditions, the convergence rates at time in both and senses are shown by virtue of the Yamada-Watanabe approximation technique. Moreover, the convergence rates over a finite time interval are also obtained. Additionally, it should be noted that the convergence rates will not be affected by the number of delay variables. Finally, we perform the numerical experiments on the stochastic volatility model to verify the reliability of the theoretical results.
Paper Structure (6 sections, 12 theorems, 111 equations, 2 figures)

This paper contains 6 sections, 12 theorems, 111 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The numerical scheme
  4. Convergence rates at $T$ in $\mathcal{L}^{1}$ and $\mathcal{L}^{2}$ sense
  5. Convergence rates over [0,T] in $\mathcal{L}^{1}$ and $\mathcal{L}^{2}$ sense
  6. Stochastic volatility model and its numerical experiment

Key Result

Lemma 2.5

Let Assumptions a1-a4 hold. Then MDSDE (msdech) admits a unique solution z(t). Moreover, for any $p\in(0,\check{p}]$,

Figures (2)

  • Figure 1: Convergence rate of TEMS for (\ref{['vq2']})
  • Figure 2: Convergence rates of TEMS for (\ref{['mul1']})-(\ref{['mul3']})

Theorems & Definitions (27)

  • Lemma 2.5
  • Lemma 2.6
  • proof
  • Remark 1
  • Remark 2
  • Lemma 3.1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • ...and 17 more