Actuarial modelling of equilibrium condition in life and pension using integral transform
This paper aims at deriving actuarial modelling of equilibrium condition in life and pension mathematics under the framework of integral transform. The specific objective is to establish net actuarial balance representing the difference between the present values of contributions and benefit outgo of the defined benefit scheme. This is the equilibrium position such the plan sponsor cannot borrow to pay plan members at the point of retirement. Our investigation confirms that the present value of benefit outgo payable by the trustees equals the present value of total contribution of the plan sponsor so that the equilibrium point is reached under the framework of integral transform.
Keywords: Integral transform, defined benefit, force of interest, equilibrium Fredholm, liability and Thiele