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*