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An Exact Solution in Series Expansion Form The 1st order differential system: ⎧ L[ ¯V 1 (x, τ)] = −L[ ¯V 0 (x, τ)] + A ′ (x, τ, 0), ¯V 1 (x, 0) = − ¯V 0 (x, 0), ⎪⎨ ¯V 1 (0, τ) + ¯S 1 (τ) = 0, ⎪⎩ ∂ ¯V 1 ∂x (0, τ) + ¯S 1 (τ) = ¯V 0 (0, τ) − ∂ ¯V 0 (0, τ) − 1, ∂x lim ¯V 1 (x, τ) = 0. x→∞ IWIF-II www.swingtum.com/institute/IWIF PPT 46/68 Song-Ping Zhu, SMAS, April 26, 2007 0-45
An Exact Solution in Series Expansion Form The nth order differential system: ⎧ L[ ¯V n (x, τ)] = n ∂n−1 A ′ ∂ n−1 , p ∣ p=0 ⎪⎨ ¯V n (x, 0) = 0, ¯V n (0, τ) + ¯S n (τ) = 0, if n ≥ 2, where ⎪⎩ ∂ ¯V n ∂x (0, τ) + ¯S n (τ) = 0, lim ¯V n (x, τ) = 0, x→∞ A ′ (x, τ, p) = 1 ∂ ¯S f ¯V (τ, p)∂ (x, τ, p). ¯S f (τ, p) ∂τ ∂x IWIF-II www.swingtum.com/institute/IWIF PPT 47/68 Song-Ping Zhu, SMAS, April 26, 2007 0-46
Page 1 and 2: Faculty of Informatics, University
Page 3 and 4: Background What is an option? What
Page 5 and 6: Review of Various solution Approach
Page 7 and 8: A Figure in Zhu and Zhang (2007b) 1
Page 17 and 18: A. Basso, M. Nardon and P. Pianca
Page 19 and 20: 1 γ=5 0.9 0.8 0.7 B(τ) 0.6 0.5 0.
Page 27 and 28: An Exact Solution in Series Expansi
Page 45: An Exact Solution in Series Expansi
Page 51 and 52: The Solution for the Option Price
Page 55 and 56: Examples and Discussion Verificatio
Page 57 and 58: Examples and Discussion 100 95 90 A
Page 59 and 60: Examples and Discussion 100 90 80 7
Page 61 and 62: Examples and Discussion 40 38 The n
Page 63 and 64: Examples and Discussion 40 35 30 Op
Page 65 and 66: Examples and Discussion Example 3:
Page 67 and 68: Examples and Discussion 100 90 80 7

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