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64 Life Contingencies
(IA)zR, = I [Cx+2Cx+1+3Cx+2+ ... -}-nCx+n-1] D,
+n) + . . .
Dx +(Mx+n_1 —Mx+n)]
Also (la) = 1 [vlx+l +2v21x+2 +3v3lx+3 + ... ] lx
= I [Dx+1 +2Dx+2 +3Dx+3 + ... ] D,
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1 |
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= |
— [Nx +Nx+1 +Nx+2 + ... ] Ds Sx Ds |
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So (Ia)xn, = |
[Dx+1+2Dx+2+3Dx+3+ ... +nDx+n] Dx |
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) + . . . +(Nx+n—1 —Nx+n)] |
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= Similarly |
[Sx—Sx+.n—nNx+n]' D, |
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Sx | |
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(Ia)x = Ds | |
and (Ia)xnl = - (Sx—Sx+n—nNx+n). D,
12. Suitable commutation symbols may be made for the valuation of assurance and annuity functions involving joint lives. For instance
axy = — [vlx+1 : Y+1 +v2lx+2 : v+2 + • • • • ]. lxy
So
= — [(Mx — Hx+n) + (Hx+i —Mx -i-)x [ (N. — Nx+n) + (N.+i —Nx+n
= [Rs —Rx+n —nMx+n]. x
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