In the lecture notes, we discussed uniform distribution of decrements (UDD) between inte- ger ages. It...

 

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In the lecture notes, we discussed uniform distribution of decrements (UDD) between inte- ger ages. It is important to understand that the UDD assumption is made with respect to the original full decre- ment model. In other words, we assumed uniform exits via all decrements simultaneously between integer ages: P=t-p², 0≤t≤ 1, integer x, for all j = 1,2,..., m. This assumption-UDD in the multiple decrement model-leads to 0j = Hatt 1-t-(1-p0)¹ Now, assume UDD in all the hypothetical single decrement models and show that (1) the forces of transition are instead given by - S² P 00 0j Hatt *G) qa 1-t.q.6), (2) for m = 3 (a triple decrement model) we have 1² ² = q 20) (1 - 5₁70) 2²/₁ 0<t<1, integer x, for all j = 1,2,..., m. 0001 ds 2) q² (³)), 0≤t≤ 1, integer z. This demonstrates that p is not linear between integer ages. Hint: Use the facts that *(5) 0<t<1, integer z, for all j = 1,2,..., m; + L'" (~p² (¹) 1) p²²) p² (³) µ²4 ds = [ (P¹) (-p) p² (³)) ds ,01 ,01 and Pr =1-s9z =1-8-9 for 0 < s < t < 1 and integer z (useful for j = 2 and j = 3 here). (3) In a triple decrement table, you are given 960 = 0.03, 900 = 0.05, loo=100,000, 461 = 90,307. Calculate d, do, and do, assuming UDD in the single decrement models between integer ages. In the lecture notes, we discussed uniform distribution of decrements (UDD) between inte- ger ages. It is important to understand that the UDD assumption is made with respect to the original full decre- ment model. In other words, we assumed uniform exits via all decrements simultaneously between integer ages: P=t-p², 0≤t≤ 1, integer x, for all j = 1,2,..., m. This assumption-UDD in the multiple decrement model-leads to 0j = Hatt 1-t-(1-p0)¹ Now, assume UDD in all the hypothetical single decrement models and show that (1) the forces of transition are instead given by - S² P 00 0j Hatt *G) qa 1-t.q.6), (2) for m = 3 (a triple decrement model) we have 1² ² = q 20) (1 - 5₁70) 2²/₁ 0<t<1, integer x, for all j = 1,2,..., m. 0001 ds 2) q² (³)), 0≤t≤ 1, integer z. This demonstrates that p is not linear between integer ages. Hint: Use the facts that *(5) 0<t<1, integer z, for all j = 1,2,..., m; + L'" (~p² (¹) 1) p²²) p² (³) µ²4 ds = [ (P¹) (-p) p² (³)) ds ,01 ,01 and Pr =1-s9z =1-8-9 for 0 < s < t < 1 and integer z (useful for j = 2 and j = 3 here). (3) In a triple decrement table, you are given 960 = 0.03, 900 = 0.05, loo=100,000, 461 = 90,307. Calculate d, do, and do, assuming UDD in the single decrement models between integer ages.