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<p>In this paper we propose an efficient third order multistep scheme for second order backward stochastic differential equations (2BSDEs for short) based on nonequidistant derivative approximation. Multistep schemes for backward stochastic differential equations (BSDEs for short) are well-known to be highly accurate. However, all the multistep schemes in the literature for solving BSDEs rely on spatial interpolation which is highly costly. By the well-chosen nonequidistant derivative approximation scheme, we manage to construct a multistep scheme avoiding spatial interpolation. We also present several numerical examples including a stochastic optimal control problem to illustrate our scheme.</p>

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A Nonequidistant Multistep Scheme for Second Order Backward Stochastic Differential Equations with Applications to Stochastic Optimal Control

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Chol-Gyu Pak,
  • Ho-Jin Hwang,
  • Mun-Chol Kim

摘要

In this paper we propose an efficient third order multistep scheme for second order backward stochastic differential equations (2BSDEs for short) based on nonequidistant derivative approximation. Multistep schemes for backward stochastic differential equations (BSDEs for short) are well-known to be highly accurate. However, all the multistep schemes in the literature for solving BSDEs rely on spatial interpolation which is highly costly. By the well-chosen nonequidistant derivative approximation scheme, we manage to construct a multistep scheme avoiding spatial interpolation. We also present several numerical examples including a stochastic optimal control problem to illustrate our scheme.