1 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 atthe start of the second year. You can choose between two types of investments, type A and typeB. In type A the annual effective rates for years 1 and 2 are given by two independent randomvariables i1, i2, identically distributed like i. In type B the annual effective rates are the samerate 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.

The probability distribution of interest rate is shown belowA 2-year investment is made where, is…

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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 46E

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