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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | https://arxiv.org/abs/1911.13070 |
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| _version_ | 1866929509937184768 |
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| author | Jiang, Lianzi Hu, Mingshang |
| author_facet | Jiang, Lianzi Hu, Mingshang |
| contents | In this paper, we study the discrete-time approximation schemes for a class of backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) which corresponds to the hedging pricing of European contingent claims. By introducing an auxiliary extended $\widetilde{G}$-expectation space, we propose a class of $θ$-schemes to discrete $G$-BSDEs in this space. With the help of nonlinear stochastic analysis techniques and numerical analysis tools, we prove that our schemes admit half-order convergence for approximating $G$-BSDE in the general case. In some special cases, our schemes can achieve a first-order convergence rate. Finally, we give an implementable numerical scheme for $G$-BSDEs based on Peng's central limit theorem and illustrate our convergence results with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_13070 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Discrete-time approximation for backward stochastic differential equations driven by $G$-Brownian motion Jiang, Lianzi Hu, Mingshang Numerical Analysis In this paper, we study the discrete-time approximation schemes for a class of backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) which corresponds to the hedging pricing of European contingent claims. By introducing an auxiliary extended $\widetilde{G}$-expectation space, we propose a class of $θ$-schemes to discrete $G$-BSDEs in this space. With the help of nonlinear stochastic analysis techniques and numerical analysis tools, we prove that our schemes admit half-order convergence for approximating $G$-BSDE in the general case. In some special cases, our schemes can achieve a first-order convergence rate. Finally, we give an implementable numerical scheme for $G$-BSDEs based on Peng's central limit theorem and illustrate our convergence results with numerical examples. |
| title | Discrete-time approximation for backward stochastic differential equations driven by $G$-Brownian motion |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1911.13070 |