Continuous Time - HW1

Continuous Time - HW1 - 1 Temple University Continuous Time...

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Unformatted text preview: 1 Temple University Continuous Time Finance HW1 2 Shreve 1.6: Moment Generating Function ( 29 ( 29 ( 29 ∫ ∫ ∫ ∫ ∞ ∞ + + +-- + ∞ ∞ + +----- ∞ ∞-- ∞ ∞ = = =- ) ( ) ( 2 2 1 2 1- ) ( 2 2 1 2 1 2 ) ( 2 1- 2 1 2 ) (- 2 1 ux 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 e (X) E dev stand and mean Normal ) ( u u x x u u u x x ux x x ux e e e e e X e x σ μ σ μ σ π σ σ μ μ σ μ σ π σ σ μ σ π σ σ μ π σ ϕ σ μ ϕ 3 Jensen’s Inequality (E(X)) ) ( (X) E dev stand and mean Normal ) ( 2 2 2 1 ϕ μ ϕ ϕ σ μ ϕ μ σ μ = = ≥ = = + u u u ux e e X e x 4 Shreve 2.6 }} , { }, , { , , { (X) ) ( d c b a i φ σ Ω = 5 Shreve 2.6 (ii) 3 1 1) ( (1) b} P{a P{b} 1) ( b} P{a P{a} (1) (1) f 1) (1, f 1) ( (1) f (1,1) f (1) (1) f y) (1, f y 1] X | E[Y 3 1 6 1 3 1 3 1 6 1 6 1 X Y X, X Y X, X Y X, y- = +- + + = ∪- + ∪ =-- + = ⋅ = = ∑ 1) ( (1) d} P{c P{d} 1) ( d} P{c P{c} (1) (-1) f 1) (-1, f 1) ( (-1) f (-1,1) f (1) (-1) f y) (-1, f y 1] X | E[Y 4 1...
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This note was uploaded on 11/23/2009 for the course FIN 5190 taught by Professor Soss during the Fall '09 term at Temple.

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Continuous Time - HW1 - 1 Temple University Continuous Time...

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