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The Application Of The Inverse Physics-Informed Neural Network In Financial Calibration Tasks | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 2، مهر 2026، صفحه 125-137 اصل مقاله (595.07 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.88390.1217 | ||
| نویسندگان | ||
| Mohamadamin Raeisi-Makiani* 1؛ Abdolsadeh Neisy2؛ Ali Safdari-Vaighani3 | ||
| 1Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran | ||
| 2Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran | ||
| 3Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Catastrophe bond؛ Deep learning؛ Inverse problem؛ Jump diffusion model؛ Physics informed neural network | ||
| مراجع | ||
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[1] A. Safdari-Vaighani and A. Mahzarnia, The evaluation of compound options based on RBF approximation methods, Engineering Analysis with Boundary Elements, 58, 112-118, (2015). [2] P. Büchel, M. Kratochwil, M. Nagl, et al., Deep calibration of financial models: turning theory into practice., Rev Deriv Res 25, 109–136 (2022). https://doi.org/10.1007/s11147-021-09183-7 [3] D. Ahmadian, O. Farkhondeh Rouz, K. Ivaz and A. Safdari-Vaighani, Robust numerical algorithm to the European option with illiquid markets, Applied Mathematics and Computation 366, 124-693, (2020). [4] G. Dimitroff, D. Röder, and C. P. Fries, Volatility model calibration with convolutional neural networks (2018), https://ssrn.com/abstract=3252432 or http://dx.doi.org/10.2139/ssrn.3252432 [5] H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Springer, (1996). [6] A. Jacot, F. Gabriel, and C. Hongler, Neural Tangent Kernel: Convergence and Generalization in Neural Networks, Advances in Neural Information Processing Systems (NeurIPS), (2018). [7] M. Jamalpour Malekabadi, A. Zakeri, et al., Application of Radial Basis Functions Meshless Method for Solving an Inverse Parabolic Problem, Journal of Mathematics and Modeling in Finance 6(1), 251-263, (2026). [8] S. Liu, A. Borovykh, L. A. Grzelak, et al., A neural network-based framework for financial model calibration, J.Math.Industry, 9 (2019). [9] S. Liu, C. W. Borovykh, and S. M. Bohte, Pricing options and computing implied volatilities using neural networks., Risks, 7(1), (2019) [10] M. Raissi, P. Perdikaris, and G.E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics, 378 , 686-707, (2019). [11] M. Siddhartha, and M. Roberto, Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs, IMA Journal of Numerical Analysis, 42(2), 981-1022, (2022). [12] M. A. Raeisi Makiani, A. Neisy, and A. Safdari-Vaighani, Pricing Catastrophe Risk Bond Using the Physics-Informed Neural Network, Computational Economics, (2025), https://doi.org/10.1007/s10614-025-11180-z [13] A. Safdari-Vaighani, D. Ahmadian, and R. Javid-Jahromi, An Approximation Scheme for Option Pricing Under Two-State Continuous CAPM. , Computational Economics, 57, 1373–1385, (2020). [14] A. N. Tikhonov, and V. Y. Arsenin, Solutions of Ill-Posed Problems, Wiley, (1977). [15] S. Wang, and X. Yu, On the convergence and generalization of physics-informed neural networks, Journal of Machine Learning Research, (2022). [16] S. Wang, Y. Teng, and P. Perdikaris, Understanding and mitigating gradient flow pathologies in physics-informed neural networks, SIAM Journal on Scientific Computing, (2021). | ||
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