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 language | English |
|---|---|
| Pages (from-to) | 519-530 |
| Number of pages | 12 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 406 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2013 Oct 15 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Copulas from the Fokker-Planck equation
AU - Choe, Hi Jun
AU - Ahn, Cheonghee
AU - Kim, Beom Jin
AU - Ma, Yong Ki
PY - 2013/10/15
Y1 - 2013/10/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84878703174&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84878703174&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2013.05.014
DO - 10.1016/j.jmaa.2013.05.014
M3 - Article
VL - 406
SP - 519
EP - 530
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -