A insurance on two independent lives (x) and (y) provides for a death benefit at the moment of the second death. The death benefit is e0.05t for death at time t. Premiums are payable until the second death, The premium is level while both are alive and reduces to one half of the initial amount upon the first death. The life (x) is subject to a constant force of mortality of 0.10 and (y) is subject to a constant force of mortality of 0.15. The force of interest is a constant 0.10. Refer to the two-life model as given Figure 19.1.

(a) Calculate for each of the first three states the annual premium and the reserve at time t.

(b) Write down the Thiele differential equations.

(c) Verify that your answers to (a) satisfy the equations in (b).