Actuarial Present Value & Variance DeMoivre Law, Annual Interest Rate - Science & Maths Assignment Help

Assignment Task

1 Question 

Calculate the actuarial present value and the variance of the present value as well as determining P according to

(i) the equivalence principle and

(ii) the portfolio premium principle (choose ↵ yourself) for an insurance product with the following characteristics: 

1. Person aged 26 

2. Receives a 40-year deferred whole life annuity due with an initial benefit of B euro each month. Each subsequent payment will be (?/4)% large than the previous one, where ? denotes the annual inflation rate 

3. There is an annual premium, payable for at most 40 years. The first premium is equal to P, while the (k+1)-th premium equals Pk+1 = P + k/1000 for k = 1, 2, 3,... 

4. Thee↵effective annual interest rate used for discounting is i%. 

5. there is an initial expense at policy issue of a% of the first benefit payment plus b% of the first premium. 

6. in the first year there is no renewal expense yet. But as of the start of the second year, the annual renewal expense equals c% of the premium of that year. 

7. Terminal expenses, incurred at the end of the quarter year of death, are, 1,000 euros inflated annually by the inflation rate of % as of the issue date. 

8. The analytical law of mortality to be used is the Generalized DeMoivre law, with ↵ = 1/6 and! = 120 

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