Unified Moment-Based Modeling of Integrated Stochastic Processes

Dial M for Simulation For years, systems of stochastic differential equations (SDEs) were simulated by discretization, inevitably introducing a bias, which can be difficult to quantify accurately. To circumvent this, some attempts have been made to simulate exactly various models from the SDE solution. These approaches prove capable of producing accurate results. A serious drawback of such an approach, nevertheless, is the implicit need to use extensive numerical methods, which make the entire simulation computationally heavy and quite impracticable. In the paper “Unified moment-based modeling of integrated stochastic processes,” Kyriakou, Brignone, and Fusai present a methodological framework based on M(oments) for the simulation of such models that overcomes earlier limitations. Theoretical results and extensive numerical experiments show that the proposed approach allows accurate simulation of complex stochastic models with low computational effort.