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1. Let S = ea+b2, where a, b are constants and b# 0, Z ~ N(0, o2). Find formulas for the following expectations in terms of a, b, o and , where (x) is the CDF of N(0,1) and K > 0 is a constant. (1) E(1{s>K}). (2) E(S1{s>K}). (3) First verify the equality max(S, K) = S1{S>K} – K1{s>K} + K; then use it and the results in (1) and (2) to find E [max(S, K)].

1. Let S = ea+b2, where a, b are constants and b# 0, Z ~ N(0, o2). Find formulas for the following expectations in terms of a, b, o and , where (x) is the CDF of N(0,1) and K > 0 is a constant. (1) E(1{s>K}). (2) E(S1{s>K}). (3) First verify the equality max(S, K) = S1{S>K} – K1{s>K} + K; then use it and the results in (1) and (2) to find E [max(S, K)].

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Let S = eat62, where a,b are constants and b + 0, Z ~ N(0,0²). Find formulas for the following expectations in terms of a, b, o and , where (x) is the CDF of N(0,1) and K > 0 is a constant. (1) E(1{s>K}). (2) E(S1{s>K}). (3) First verify the equality max(S, K) = S1{s>K} – K1{s>K}+ K; then use it and the results in (1) and (2) to find E [max(S, K)].
Transcribed Image Text:1. Let S = eat62, where a,b are constants and b + 0, Z ~ N(0,0²). Find formulas for the following expectations in terms of a, b, o and , where (x) is the CDF of N(0,1) and K > 0 is a constant. (1) E(1{s>K}). (2) E(S1{s>K}). (3) First verify the equality max(S, K) = S1{s>K} – K1{s>K}+ K; then use it and the results in (1) and (2) to find E [max(S, K)].
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