Unified Moment-Based Modeling of Integrated Stochastic Processes

• 成果类型: Article
• 署名作者: Kyriakou, Ioannis; Brignone, Riccardo; Fusai, Gianluca
• 署名单位: City St Georges, University of London; University of Freiburg; University of Eastern Piedmont Amedeo Avogadro; City St Georges, University of London
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2422
• 发表日期: 2024
• 页码: 1630-1653
• 关键词: exact simulation; efficient simulation; generating function; Asian options; volatility; jumps; distributions; derivatives; heston; time

摘要

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 schemes.