Tutorial 4

# Tutorial 4 - T| v T 6 For a 10-year deferred life...

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FIN 3220A Actuarial Models I Tutorial 4 26 October 2005 1. You are given: (i) a x = 10 (ii) 2 a x = 7.375 (iii) Var(a T| ) = 50 Find A x . 2. You are given the following information for a temporary life annuity due issued to (x): Year t Amount of payment p x+t 0 2 0.8 1 3 0.75 2 4 0.5 Calculate the variance of the r.v. which represents the PV of the indicated payments, using v = 0.9 3. Consider a group of individuals all age x, which is 50% male and 50% female. You are given the following values for each of the subgroups. All values were calculated using δ= 0.1. Male Female A x 0.15 0.09 Var(a T| ) 5 4 Find a x and Var(a T| ) for an individual chosen at random from the group. 4. You are given: (i) Var(a T| ) = 100/9 (ii) µ(x+t) = k, for all t (iii) δ = 4k Calculate k. 5. T is the r.v. for the future lifetime of (x). Find Cov[a

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Unformatted text preview: T| , v T ]. 6. For a 10-year deferred life annuity-due of 1 per year on (60): (i) mortality follows de Moivre's law with ω = 100 (ii) i = 0 Calculate the probability that the sum of the payments made under the annuity will exceed the APV at issue of the annuity. FIN 3220A Actuarial Models I Tutorial 4 26 October 2005 7. Consider the following present value random variables. where K is the curtate future lifetime of (x): Y = a K+1| Z = a K+1| for 0 &amp;lt; K &amp;lt; n, Z = a n| for K &amp;gt; n It is given that: (i) i = 0.06 (ii) A x = 0.20755 (iii) a x:n-1| = 6 Find E[Y] - E[Z] 8. For a 5-year deferred whole life annuity-due of 1 on (x): (i) μ (x+t) = 0.01 (ii) i = 0.04 (iii) a x: 5| = 4.452 (iv) The random variable S denotes the sum of the annuity payments Calculate P[S &amp;gt; 5| a x ]. .. .. .. .. .....
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Tutorial 4 - T| v T 6 For a 10-year deferred life...

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