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Let i be a random variable with the following discrete distribution: i is 5% with probability 10% with probability and -4% with probability 1. Consider a 2-year investment, where you invest £100 at the start for the first year and £50 at the start of the second year. You can choose between two types of investments, type A and type B. In type A the annual effective rates for years 1 and 2 are given by two independent random variables 11, 12, identically distributed like i. In type B the annual effective rates are the same rate i. (a) Which investment type would you choose if you wanted to maximise the expected accu- mulate value after 2 years? Give a proof. (b) Which investment type would you choose if you wanted to minimise your risk after 2 years? Assume that risk is measured as the variance of your accumulated value. Give a proof.

Let i be a random variable with the following discrete distribution: i is 5% with probability 10% with probability and -4% with probability 1. Consider a 2-year investment, where you invest £100 at the start for the first year and £50 at the start of the second year. You can choose between two types of investments, type A and type B. In type A the annual effective rates for years 1 and 2 are given by two independent random variables 11, 12, identically distributed like i. In type B the annual effective rates are the same rate i. (a) Which investment type would you choose if you wanted to maximise the expected accu- mulate value after 2 years? Give a proof. (b) Which investment type would you choose if you wanted to minimise your risk after 2 years? Assume that risk is measured as the variance of your accumulated value. Give a proof.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let i be a random variable with the following discrete distribution: i is 5% with probability , 10% with probability and -4% with probability . Consider a 2-year investment, where you invest £100 at the start for the first year and £50 at the start of the second year. You can choose between two types of investments, type A and type B. In type A the annual effective rates for years 1 and 2 are given by two independent random variables i1, i2, identically distributed like i. In type B the annual effective rates are the same rate i. (a) Which investment type would you choose if you wanted to maximise the expected accu- mulate value after 2 years ? Give a proof. (b) Which investment type would you choose if you wanted to minimise your risk after 2 years? Assume that risk is measured as the variance of your accumulated value. Give a proof.
Transcribed Image Text:Let i be a random variable with the following discrete distribution: i is 5% with probability , 10% with probability and -4% with probability . Consider a 2-year investment, where you invest £100 at the start for the first year and £50 at the start of the second year. You can choose between two types of investments, type A and type B. In type A the annual effective rates for years 1 and 2 are given by two independent random variables i1, i2, identically distributed like i. In type B the annual effective rates are the same rate i. (a) Which investment type would you choose if you wanted to maximise the expected accu- mulate value after 2 years ? Give a proof. (b) Which investment type would you choose if you wanted to minimise your risk after 2 years? Assume that risk is measured as the variance of your accumulated value. Give a proof.
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