(b) Let T> 0 and consider the function g : [0, T] x R which satisfies g(t, B₁) = E[B²|Ft]. Write down the PDE and terminal conditions satisfied by g. (c) Solve the PDE from part b). (Hint: assume g is of the form g(t, x) a(t) + b(t)x+ c(t)x² where a, b, and c are deterministic functions.) =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 43E
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Please solve both part

 

(b) Let T > 0 and consider the function g : [0, T] × R which satisfies
g(t, Bt) = E[B²|Ft] .
Write down the PDE and terminal conditions satisfied by g.
(c) Solve the PDE from part b). (Hint: assume g is of the form g(t, x)
a(t) + b(t)x+ c(t)x² where a, b, and c are deterministic functions.)
Transcribed Image Text:(b) Let T > 0 and consider the function g : [0, T] × R which satisfies g(t, Bt) = E[B²|Ft] . Write down the PDE and terminal conditions satisfied by g. (c) Solve the PDE from part b). (Hint: assume g is of the form g(t, x) a(t) + b(t)x+ c(t)x² where a, b, and c are deterministic functions.)
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