 Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity securities into the sum of orthogonal risks using a risk basis.
<meaning-changed>  Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity securities into the sum of orthogonal risks using a risk basis.
 Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity securities into the sum of "non-correlated" risks using a risk basis.