SOLVING HIGH-DIMENSIONAL SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DEEP BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Parabolic partial differential equations are partial differential equations that can describe many phenomena, such as the movement of particles, heat conduction, until derivative pricing in finance. The nonlinear terms which are not originated in the highest order and the addition of spatial dimensi...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/47752 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Parabolic partial differential equations are partial differential equations that can describe many phenomena, such as the movement of particles, heat conduction, until derivative pricing in finance. The nonlinear terms which are not originated in the highest order and the addition of spatial dimension can model more realistic and more complex problems. However, at the same time, this will make the analytical and numerical computation harder. Therefore, we require a method to solve these equations. Deep Backward Stochastic Differential Equations is one of the methods to solve high-dimensional semilinear parabolic partial differential equations using artificial neural networks. This study will cover how to build neural networks for solving high-dimensional semilinear parabolic partial differential equations, which tested for semilinear parabolic partial differential equations with explicit solutions and Black-Scholes equations with default risk as well as comparing this method using some different artificial neural networks architecture. |
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