I work for a company that lately has assigned me to calculate actuarial liabilities of its employees and pensioners. I have chosen the PUC method for calculating the liabilities and some calculations are done, based on suggestions of my supervisor. Recently, I have some doubts about the calculation. In fact, the policy of the company is that if a male employee dies, a death benefit is payable as a pension to his wife,as long as she survives. the same is true for the retirees.Up to now, my calculation is based on:

sigma (v^t *t_p_x)+ sigma(k*(v^t)*(1-t_p_x)*t_p_y)

where 1<= t<=109-x, x is the age of employee and y is the age of his wife

but , as I mentioned, I am suspicious what if the right formula is:

sigma (v^t *t_p_x)+ sigma(k*(v^t)*(1-t_p_x)*t_p_y)*sigma (v^j *j_p_(y+x))
since it is said after death of the husband, at any age, his wife receives the benefits and 1<= t<=109-x and 1<= j<=109-y-t

please help.

ps. the first part of the summations is not considered when calculating the death benefit and "k" is the portion of the benefit payable to his wife.