Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by

$$C(u_1,…,u_d)\leq \min\{u_1,..,u_d\}.$$

Is there a similar (in the sense that it depends on the marginal densities) upper bound for the copula density $c(u_1,…,u_d)$ instead of the CDF?

Any reference would be greatly appreciated.

Answer

Generally speaking, no there isn’t. For example, in the bivariate gaussian copula case, the quantity in the exponent has a saddle point at (0,0), and therefore explodes to infinity in two directions.
If you come across a class of copula densities that are in fact bounded, please let me know!

Attribution
Source : Link , Question Author : Coppola , Answer Author : MHankin

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