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)].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84a310e0-6f97-4def-b827-628265d91c57%2Fe7f7dd88-fcda-429a-a82c-f766012e3d6b%2F1fc3poi_processed.png&w=3840&q=75)
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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