An improved physics-informed neural network for valuing American lookback options under regime-switching jump-diffusion models

This study addresses the computational challenges inherent in valuing American lookback options within a regime-switching jump-diffusion (RSJD) framework. We first formulate the pricing problem as a system of coupled partial integro-differential equations (PIDEs) structured as linear complementarity problems (LCPs), rigorously capturing the interplay of path dependency, early exercise rights, and market regime transitions. To solve this complex free-boundary problem, we propose an improved physics-informed neural network (I-PINN). This novel architecture augments the standard PINN framework by incorporating a hard-coded terminal condition to guarantee theoretical consistency, a dynamic self-adaptive weighting scheme to balance the composite loss function, and the Fischer–Burmeister function to provide an exact semismooth reformulation of the LCP constraints. For accuracy assessment, the proposed method is benchmarked primarily against independently refined finite-difference reference solutions obtained from a reduced one-dimensional solver for floating-strike options and a full two-dimensional solver for fixed-strike options. The results show that the I-PINN attains competitive pricing accuracy, improved training stability relative to the standard PINN, and efficient post-training evaluation across the state domain. Furthermore, the practical applicability of the framework is validated through the accurate computation and analysis of key risk sensitivities, establishing it as a robust instrument for modern risk management.