Lets say \(u_{xy}^{01}= 0.01 +0.05*1.05^x\) and \(u_{xy}^{02}= 0.01 +0.05*1.05^y\). Where x is the male and y the female. And state 0 is both alive, state 1 is male dead, female alive and state 2 is female dead, male alive.

I would like to calculate

$$\overline{A}_{xy}^{01} = \int_0^\infty e^{-\delta t} {}_{t}p^{00}_{xy} \mu_{x+t;y+t}^{01} dt$$

Where

$${}_{t}p^{00}_{xy} = e^{-\int_0^t (\mu_{x+s;y+s}^{01} + \mu_{x+s;y+s}^{02}) ds}$$

(Please correct me if any of the above formulae are wrong)

My issue comes in when we are given \(u_{xy}^{01}\) instead of \(\mu_{x+t;y+t}^{01} \) and the same goes for \(u_{xy}^{02} \), how do I use the above equations and those integrals.