FM5002-HW6-3.7.12 - Financial Mathem atics 5002 Hom ework...

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Financial Mathematics 5002 : Homework 6 (0044) Due on 7 March 2012 Scot Adams Solutions 0044 M 1 . Compute I L x 4 P 2 x 2 R E M x 2 2 D x. Using the results from class, I L x 4 P 2 x 2 R E M x 2 2 D x e I x 4 E M x 2 2 D x P 2 I x 2 E M x 2 2 D x eE M x 2 2 L M 5 x M x 3 R P 5 2 Π C L x R . M 2 . Compute I 4 I E M x 2 2 D I 4 I E M x 2 2 D x e 2 Π C L M 4 R . M 3 . Compute I 9 I E 8x E M x 2 2 D We complete the square : I 9 I E 8x E M x 2 2 D x e I 9 I E M L x M 8 R 2 2 P 32 D x I 9 I E M L x M 8 R 2 2 D x e E I 1 I E M u 2 2 D u 2 Π C L M 1 R . M 4 . Compute I 4 I L 3 E 8x M 3 E 8 R E M x 2 2 D From the previous problems, I 4 I L 3 E 8x M 3 E 8 R E M x 2 2 D x e 3 I 4 I E 8x E M x 2 2 D x M 3 E 8 I 4 I E M x 2 2 D x e 3 E 2 Π C L 4 R M 3 E 8 2 Π C L M 4 R . M 5 . Compute I MI I L 3 E 8x M 3 E 8 R P E M x 2 2 D L 3 E 8x M 3 E 8 R G 0 when x G 1, so that I I L 3 E 8x M 3 E 8 R P E M x 2 2 D x e I 1 I L 3 E 8x M 3 E 8 R E M x 2 2 D x e 3 E 2 Π C L 7 R M 3 E 8 2 Π C L M 1 R , from 0044 M 4.
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