Approximation approach for backward stochastic Volterra integral equations

Kutorzi Edwin Yao; Mahvish Samar; Yufeng Shi; Kutorzi Edwin Yao; Mahvish Samar; Yufeng Shi

doi:10.3934/mmc.2024031

Mathematical Modelling and Control

2024, Volume 4, Issue 4: 390-399. doi: 10.3934/mmc.2024031

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Research article

Approximation approach for backward stochastic Volterra integral equations

1.
Institute for Financial Studies, Shandong University, Ji'nan 250100, China
2.
School of Mathematics, Shandong University, Ji'nan 250100, China
3.
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

Received: 06 September 2023 Revised: 20 May 2024 Accepted: 28 June 2024 Published: 14 November 2024

In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block pulse functions (BPFs) and the related stochastic operational matrix of integration. Additionally, we developed considerations for Lipschitz and linear growth, along with linearity conditions, to illustrate error and convergence analysis. We compared the solutions we obtain the values of exact and approximate solutions at selected points with a defined absolute error. The computations were performed using MATLAB R2018a.
- BSVIEs,
- BSDEs,
- BPFs,
- operational matrix,
- collocation approximation
Citation: Kutorzi Edwin Yao, Mahvish Samar, Yufeng Shi. Approximation approach for backward stochastic Volterra integral equations[J]. Mathematical Modelling and Control, 2024, 4(4): 390-399. doi: 10.3934/mmc.2024031

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Abstract

In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. We used Newton's technique to solve a particular BSVIE by employing block pulse functions (BPFs) and the related stochastic operational matrix of integration. Additionally, we developed considerations for Lipschitz and linear growth, along with linearity conditions, to illustrate error and convergence analysis. We compared the solutions we obtain the values of exact and approximate solutions at selected points with a defined absolute error. The computations were performed using MATLAB R2018a.

References

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