Unified Moment-Based Modeling of Integrated Stochastic Processes

In this paper, we present a new method for simulating integrals of stochastic processes. We focus on the nontrivial case of time integrals, conditional on the state variable levels at the endpoints of a time interval through a moment-based probability distribution construction. We present different classes of models with important uses in finance, medicine, epidemiology, climatology, bioeconomics, and physics. The method is generally applicable in well-posed moment problem settings. We study its convergence, point out its advantages through a series of numerical experiments, and compare its performance against existing schemes.

Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2422.