Document Type : Research Article
Authors
1 Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran
2 Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran
3 Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran
Abstract
In the calibration of a financial model, the process is an optimization task that can be viewed as an inverse problem. Solving this problem typically necessitates having an appropriate pricing function. With recent breakthroughs in machine learning, i.e., physics informed neural networks (PINNs), a cutting-edge approach that combines artificial neural networks with fundamental physical principles, the task can be efficiently implemented by the inverse physics-informed neural network (iPINN). This paper centers on solving an inverse problem for a financial P(I)DE model by means of iPINN. Firstly, we model the bond price dynamics of catastrophe bonds (CAT bonds) and derive a partial integro-differential equation (PIDE) through a no-arbitrage strategy within the framework of an incomplete market. Thereafter, we employ the iPINN to estimate a specific parameter of the model, namely the market price of risk. The market price of risk is treated as a global learnable parameter and is embedded directly into the PIDE operator. The proposed iPINN is evaluated through three practically meaningful criteria: repricing error, parameter stability, and PIDE residual consistency. The outcomes demonstrate that iPINNs have the capability to solve the inverse problem effectively, and this technique could be applied broadly to real-world data.
Keywords
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