The purpose of this problem is to solve the following PDE using a numerical simulation.{af(t, x) + (1 − x)=-Ətaf 10²ƒ+მე 2 მე2= 0f(ln(2), x)=ex(a) The equation above corresponds to a Feynman-Kac formula. Identify the stochasticprocess (X)20 and the expectation that would correspond to f(t, x) explicitly.(b) Use a numerical simulation of (X+) above to approximate the values of f(0, x) at 20discrete points for x, uniformly spaced in the interval [0,2]. Submit a graph of yoursolution.(c) How would you proceed to estimate the function f(0.1, x). (Briefly explain yourmethod, you do not need to do it.)Extra question: You can explicitly determine the function in (b) (either as a conditionalexpectation or by solving the PDE). Compare the theoretical answer to your solution.

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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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INV 2-3d Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =0.02+0.80RM+eHD R-squared =0.6 RML =-0.03+1.50RM+eML R-squared =0.4 σM =0.20 where M is S&P/TSX Comp Index and RX is the excess return of stock X. d. For portfolio P with investment proportion of 0.3 in HD and 0.7 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.
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