Unified Moment-Based Modelling of Integrated Stochastic Processes

In this paper we present a new general 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, based on a moment-based probability distribution construction. We present different classes of models with important usages in finance, medicine, epidemiology, climatology, bioeconomics and physics. We highlight the benefits of our method and benchmark its performance against existing schemes.