Hey!
You find my question below and the other pages included is just derivations of the equations. Since I don’t know if you need them I just included them because I have them! Just ignore them if you don’t need them!
Question:
Given the yearly benefit of q = 12 x 10 000, the interest rate assumption of 4,2 % and mortality assumptions;
the guaranteed amount F, can now be calculated through equation (25) (the last equation below).
So I need you to calculate F for me if possible.
Remarks:
In the text I have written x-hat(v). this is for the x symbol that have a v on top of it.
You might not need this information but z is 65 and t0 is 40…

3.2 Stochastic Cash Flow
The cash flow describes the amount and the time for in- and out payments that occurred or will occur in the future. It will be regarded as continuous since that is the most common way in practice. A cash flow is stochastic if it for any time depends on an uncertain, stochastic outcome ?. For instance, you are promised 1 000 SEK in ten years from now given that you are alive at that point. The sample space for this event would be O = {dead, alive} and the payment will only occur if ?= alive. Here focus lie on a cash flow that is a function of a stochastic variable Y = Y(?), ? ?O , on the form
Where ƒ are a deterministic function that is most commonly used in insurance models. A cash flow in longevity insurance depends not only on age but also on a stochastic life span. If we let x be a deterministic cash flow we can get a stochastic cash flow x-bar through
(9) The indicator function is to be regarded as;
(10)
or in other words, as a function on O. In de following the outcome ? will be left out from the definition. The discounted value of the amount x-bar(u)du at age t is given by
(11)
Where the rate rt now is allowed to be stochastic. Summarizing all contributions to present value for all future ages t gives us; (12)
The expected value given that the individual are alive at…