Unified Moment-Based Modeling of Integrated Stochastic Processes.

The article focuses on a novel moment-based simulation methodology for integrated stochastic processes, particularly conditional stochastic integrals arising in complex models such as stochastic volatility, epidemiology, bioeconomics, and physics. It addresses limitations of traditional discretization and exact simulation methods by fitting Pearson distribution curves to the conditional distributions uniquely determined by their moments, thereby avoiding computationally intensive Laplace transform inversions. The approach includes an efficient algorithm for computing moments via numerical inversion of modified moment-generating functions, enabling fast and accurate random number generation for a wide range of models, including Heston, SABR, OU-SV, 3/2, 4/2, Bates, and jump-diffusion processes. Theoretical error bounds are derived to quantify approximation accuracy, and extensive numerical experiments demonstrate significant computational speed-ups and high precision in pricing path-independent and path-dependent derivatives, as well as applications in bioeconomic and physical systems modeled by linear and nonlinear stochastic differential equations.