Transform Analysis for Markov Processes and Applications: An Operator-based Approach

27 Pages Posted: 7 Mar 2019

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Chihoon Lee

Stevens Institute of Technology

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China.

Lingjiong Zhu

University of Minnesota - Minneapolis

Date Written: February 17, 2019

Abstract

We establish a novel duality relationship between continuous and discrete non-negative additive functionals of stochastic (not necessarily Markovian) processes and their right inverses. For general Markov processes, we further extend and develop a theoretical and computational framework for the transform analysis via an operator-based approach, i.e. through the infinitestimal generators. More precisely, we characterize the joint double transforms of additive functionals of Markov processes and the terminal values in both discrete and continuous time. In particular, under the continuous-time Markov chain (CTMC) setting, we obtain single Laplace transforms for continuous/discrete additive functionals and their inverses. Lastly, we discuss the potential applications of the proposed transform methodology in various contextual areas in finance and queuing theory within operations research.

Keywords: Transform analysis, Asset pricing, Occupation time, Markov Process, Finance

JEL Classification: G12, G13

Suggested Citation

Cui, Zhenyu and Lee, Chihoon and Liu, Yanchu and Zhu, Lingjiong, Transform Analysis for Markov Processes and Applications: An Operator-based Approach (February 17, 2019). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=3336238 or http://dx.doi.org/10.2139/ssrn.3336238

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Chihoon Lee

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China. ( email )

Haizhu District,
Guangzhou, China.
Guangzhou, Guangdong 510275
China

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

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