Before revision:  This constitutes our first main original contribution, while the second main contribution lies in describing, as explicit as possible, the optimal strategy when hedging mortalityrisks using the optional martingale representation .
After revision:  This constitutes our first principal novel contribution. 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. One of the components of this basis is a new martingale, in the large filtration, that possesses nice features. Hence, the dynamics of mortality and longevity securities used in the securitization is described without mortality specification, and this constitutes our second novel contribution. Our third main contribution resides in finding explicitly the risk-minimization strategy as well as the corresponding undiversified risk for a largest class of mortality/longevity linked liabilities with or without the mortality securitization .