Copulas from the Fokker-Planck equation

Hi Jun Choe, Cheonghee Ahn, Beom Jin Kim, Yong Ki Ma

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We develop a theoretical framework addressing the joint distribution and provide a general equation for time-dependent copulas related to stochastic processes that arise in finance. The copula is a function that links univariate distributions to a joint multivariate distribution. The tractability and importance of a copula lie in the inference function for margins (IFM) method which is very suitable to use to achieve an understanding of many correlated statistical objects. We derive a parabolic equation for the copula governing the stochastic behavior with independent drifts and volatilities of multivariate objects. In fact, the Fokker-Planck equation for the stochastic differential equations with independent drifts and volatilities is modeled for the IFM. We also present numerical results which illustrate several sensitivity analyses of our scheme.

Original languageEnglish
Pages (from-to)519-530
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume406
Issue number2
DOIs
Publication statusPublished - 2013 Oct 15

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Fokker Planck equation
Copula
Fokker-Planck Equation
Joint Distribution
Volatility
Margin
Finance
Random processes
Link Function
Tractability
Multivariate Distribution
Differential equations
Parabolic Equation
Univariate
Stochastic Equations
Stochastic Processes
Differential equation
Numerical Results
Object

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Choe, Hi Jun ; Ahn, Cheonghee ; Kim, Beom Jin ; Ma, Yong Ki. / Copulas from the Fokker-Planck equation. In: Journal of Mathematical Analysis and Applications. 2013 ; Vol. 406, No. 2. pp. 519-530.
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Copulas from the Fokker-Planck equation. / Choe, Hi Jun; Ahn, Cheonghee; Kim, Beom Jin; Ma, Yong Ki.

In: Journal of Mathematical Analysis and Applications, Vol. 406, No. 2, 15.10.2013, p. 519-530.

Research output: Contribution to journalArticle

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