A general framework for time-changed Markov processes and applications

Zhenyu Cui, J. Lars Kirkby, Duy Nguyen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we propose a general approximation framework for the valuation of (path-dependent) options under time-changed Markov processes. The underlying background process is assumed to be a general Markov process, and we consider the case when the stochastic time change is constructed from either discrete or continuous additive functionals of another independent Markov process. We first approximate the underlying Markov process by a continuous time Markov chain (CTMC), and derive the functional equation characterizing the double transforms of the transition matrix of the resulting time-changed CTMC. Then we develop a two-layer approximation scheme by further approximating the driving process in constructing the time change using an independent CTMC. We obtain a single Laplace transform expression. Our framework incorporates existing time-changed Markov models in the literature as special cases, such as the time-changed diffusion process and the time-changed Lévy process. Numerical experiments illustrate the accuracy of our method.

Original languageEnglish (US)
Pages (from-to)785-800
Number of pages16
JournalEuropean Journal of Operational Research
Volume273
Issue number2
DOIs
StatePublished - Mar 1 2019

Fingerprint

Markov Process
Markov processes
Continuous-time Markov Chain
Time Change
Additive Functionals
Transition Matrix
Approximation Scheme
Valuation
Laplace transform
Diffusion Process
Markov Model
Functional equation
Laplace transforms
Numerical Experiment
Framework
Markov process
Transform
Path
Dependent
Approximation

All Science Journal Classification (ASJC) codes

  • Information Systems and Management
  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research

Cite this

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A general framework for time-changed Markov processes and applications. / Cui, Zhenyu; Lars Kirkby, J.; Nguyen, Duy.

In: European Journal of Operational Research, Vol. 273, No. 2, 01.03.2019, p. 785-800.

Research output: Contribution to journalArticle

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