Recall the definitions of the actuarial notations. Prove the following identities: (a) a| + Snt =...

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Recall the definitions of the actuarial notations. Prove the following identities: (a) a₁| + Sn—t = vt sm for 0≤t≤n. (b) v2v2 + 3v3 + +2v2n−2+v2n-1 + (n − 1)vn−1 + nv² + (n − 1)vn+1 + (n − 2)vn+2 + an⚫än. (c) (Ia) ап = 1 (d) f[0,1] 1+r1 f[1,2] (1+r)² n d isn f[n−1,n] (1+rn) n 1 (1+rn) n , - where rk is the k-th spot rate and f[k−1,k] is the annual forward rate between time k − 1 and k. Please select file(s) Select file(s) Recall the definitions of the actuarial notations. Prove the following identities: (a) a₁| + Sn—t = vt sm for 0≤t≤n. (b) v2v2 + 3v3 + +2v2n−2+v2n-1 + (n − 1)vn−1 + nv² + (n − 1)vn+1 + (n − 2)vn+2 + an⚫än. (c) (Ia) ап = 1 (d) f[0,1] 1+r1 f[1,2] (1+r)² n d isn f[n−1,n] (1+rn) n 1 (1+rn) n , - where rk is the k-th spot rate and f[k−1,k] is the annual forward rate between time k − 1 and k. Please select file(s) Select file(s)

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