Unfortunately, despite using a discount function quantified via an STFN, the spot rate is not an STFN because it is not a linear function of [f.
In the Appendix we demonstrate that its approximation by means of an STFN is
If the amounts and the cash flows are given by STFNs, 19 will not be an STFN but it can be approximated by an STFN from (9).
if they are the amounts paid by a bond), and to obtain their present value we use a discount function quantified via an STFN like (25), (47) can be written as
So, if the discount function estimated by an STFN, the net single premium for an n-year pure endowment, (49), is reduced to
Moreover, we will allow the total amount of the liabilities, L, to be estimated by an STFN, i.
To do this, we must, in the fuzzy recursive calculation (68), use the approximating formula (11) for multiplication between two STFN.
Therefore, the whole IBNR reserve is the STFN R = ([R.
Bearing in mind that the value of the discount function for any t is an STFN [f.
4) Clearly, the subtraction of two STFNs is an STFN because the subtraction is the sum of the first FN with the second one multiplied by -1.