Adaptive PIRBFNN networks for multi-asset options

The valuation of financial options with multiple underlying assets represents one of the most complex challenges in computational financial mathematics. The Black-Scholes partial differential equation becomes a high-dimensionality problem when considering asset baskets, exchange options, or exotic derivatives. Traditional numerical methods, such as finite differences or finite elements, suffer from the curse of dimensionality, becoming impractical beyond three or four dimensions. In this context, physics-informed neural networks (PINNs) have emerged as a promising alternative, but they often require rigid architectures and costly training. A recent evolution is the PIRBFNN approach, which combines the efficiency of radial basis functions (RBFs) with the learning capability of PINNs, incorporating adaptive refinement of hidden neurons based on the PDE residual. This technique allows for precise handling of non-smooth payoff conditions, such as those appearing in European put options, two-asset exchange options, and four-asset basket call options, validating its effectiveness in multidimensional scenarios. The adaptability of the method significantly reduces the number of required collocation points and improves convergence, opening the door to real-time applications for AI for companies in the financial sector. In an environment where speed and accuracy are critical, implementing such solutions requires robust and scalable platforms. At Q2BSTUDIO we develop custom software with artificial intelligence that integrates advanced models like PIRBFNN into cloud infrastructures, whether with AWS and Azure cloud services for distributed processing or with AI agents that automate calibration and backtesting. Additionally, our cybersecurity solutions protect sensitive portfolio data, while Power BI dashboards and business intelligence services enable real-time visualization of valuation metrics. We combine custom applications with a practical approach: from implementing hyperparameter optimization algorithms to connecting with real-time market sources. The synergy between cutting-edge numerical methods and scalable enterprise platforms is the key to bringing academic innovation to everyday financial production.