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Problem 2. Feynman-Kac application We consider the stochastic process (X+)+20 given by X₁ = et, where (W₁) is a Brownian motion. (a) Determine the stochastic differential equation satisfied by the process (X+). (b) We want to determine g(t, X₁) = EXF] Use Feynman-Kac formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in x. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution.

Problem 2. Feynman-Kac application We consider the stochastic process (X+)+20 given by X₁ = et, where (W₁) is a Brownian motion. (a) Determine the stochastic differential equation satisfied by the process (X+). (b) We want to determine g(t, X₁) = EXF] Use Feynman-Kac formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in x. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Problem 2. Feynman-Kac application We consider the stochastic process (X+)+20 given by X₁ = et, where (W₁) is a Brownian motion. (a) Determine the stochastic differential equation satisfied by the process (X+). (b) We want to determine g(t, X₁) = EXF] Use Feynman-Kac formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in x. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution.
Transcribed Image Text:Problem 2. Feynman-Kac application We consider the stochastic process (X+)+20 given by X₁ = et, where (W₁) is a Brownian motion. (a) Determine the stochastic differential equation satisfied by the process (X+). (b) We want to determine g(t, X₁) = EXF] Use Feynman-Kac formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in x. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution.
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