Hi Jaya
Yes, you're correct to say that reserves are basically the sum kept aside by an insurance company for a contract to meet expected future outgo in excess of the expected future income.
And yes, you're correct to say that the asset share for an endowment will grow over time as premiums are paid and interest is earned.
However it's not correct to say that reserves decrease over time as sufficient assets are built up. When we calculate the reserves we need to allow for the full cost of the benefits and not just the cost in excess of the assets built up.
A simple example might help. Consider a ten year pure endowment. We will ignore mortality, expenses and investment return for simplicity. The sum assured is 100 and the annual premium is 10.
At time zero, after the first premium is paid the reserve is the value of the benefits (100) minus the value of the future premiums (9*10), so V0 = 10. So if we hold the reserve of 10 and receive future premiums of 90 we have enough to pay the claim of 100.
At time one, after the second premium is paid the reserve is the value of the benefits (100) minus the value of the future premiums (8*10), so V0 = 20. So if we hold the reserve of 20 and receive future premiums of 80 we have enough to pay the claim of 100.
At time two, after the third premium is paid the reserve is the value of the benefits (100) minus the value of the future premiums (7*10), so V0 = 30. So if we hold the reserve of 30 and receive future premiums of 70 we have enough to pay the claim of 100.
So you can see that the reserves do increase over time as premiums are paid. It is these premiums that give the insurer the assets to back the increased reserves.
I hope this helps.
Best wishes
Mark