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Volume 19, Issue 6
Probabilistic Numerical Approach for PDE and Its Application in the Valuation of European Options

Dong-Sheng Wu

J. Comp. Math., 19 (2001), pp. 591-600.

Published online: 2001-12

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  • Abstract

This paper suggests a probabilistic numerical approach for a class of PDE. First of all, by simulating Brownian motion and using Monte-Carlo method, we obtain a probabilistic numerical solution for the PDE. Then, we prove that the probabilistic numerical solution converges in probability to its solution. At the end of this paper, as an application, we give a probabilistic numerical approach for the valuation of European Options, where we see volatility $\sigma$, interest rate $r$ and divident rate $D_0$ as functions of stock $S$, respectively. 

  • Keywords

Brownian motion, Probabilistic numerical solution, European options.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-591, author = {Wu , Dong-Sheng}, title = {Probabilistic Numerical Approach for PDE and Its Application in the Valuation of European Options}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {6}, pages = {591--600}, abstract = {

This paper suggests a probabilistic numerical approach for a class of PDE. First of all, by simulating Brownian motion and using Monte-Carlo method, we obtain a probabilistic numerical solution for the PDE. Then, we prove that the probabilistic numerical solution converges in probability to its solution. At the end of this paper, as an application, we give a probabilistic numerical approach for the valuation of European Options, where we see volatility $\sigma$, interest rate $r$ and divident rate $D_0$ as functions of stock $S$, respectively. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9011.html} }
TY - JOUR T1 - Probabilistic Numerical Approach for PDE and Its Application in the Valuation of European Options AU - Wu , Dong-Sheng JO - Journal of Computational Mathematics VL - 6 SP - 591 EP - 600 PY - 2001 DA - 2001/12 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9011.html KW - Brownian motion, Probabilistic numerical solution, European options. AB -

This paper suggests a probabilistic numerical approach for a class of PDE. First of all, by simulating Brownian motion and using Monte-Carlo method, we obtain a probabilistic numerical solution for the PDE. Then, we prove that the probabilistic numerical solution converges in probability to its solution. At the end of this paper, as an application, we give a probabilistic numerical approach for the valuation of European Options, where we see volatility $\sigma$, interest rate $r$ and divident rate $D_0$ as functions of stock $S$, respectively. 

Wu , Dong-Sheng. (2001). Probabilistic Numerical Approach for PDE and Its Application in the Valuation of European Options. Journal of Computational Mathematics. 19 (6). 591-600. doi:
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