Nonlinear PDEs risen when solving some optimization problems in finance, and their solutions
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and discuss the properties of these PDEs. We also demonstrate how to solve them numerically in a general case, and analytically in some particular case.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
On the Matching Equations of Kinetic Energy Shaping in IDA-PBC
Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial d…
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of…
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator representation with regularization from d…
Long-time Integration of Nonlinear Wave Equations with Neural Operators
Neural operators have shown promise in solving many types of Partial Differential Equations (PDEs). They are significantly faster compared to traditional numerical solvers once they have been trained with a certain amoun…
MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, …