need help!!Pleaaaaaaaaaaasssssssssseeeeeeee

[fireranger]

hi guys
I am new here. our university just started the course so its not certified yet so I am not sure where these questions should go. but I could really use your help as our teacher isnt very good so i have no idea whats going on.
Thanks

1. An investor has wealth X and invests a proportion (alpha) in a risky asset
that will increase in value by y% (so that an investment of 1 would
increase to 1+y) with probability p and fall to zero with probability
1 − p. The amount not invested in the risky asset will neither increase
nor decrease in value.
(a) If the investor has a utility function U(w) = ln(w) then show that
expected utility is maximimized by maximizing
lnX + p ln(1 + alpha*y) + (1 − p) ln(1 − alpha)

(b) Hence show that expected utility is maximized when
alpha = {yp- (1-p)}/{y}
What does the numerator represent?
(c) Find the proportion of the investor’s wealth that he would be prepared
to invest in an asset that doubled in value with probability 5/6 but became worthless with probability 1/6.

Q2. Show that the utility function U(w) = pw has
(a) decreasing absolute risk aversion.
(b) constant relative risk aversion.

Q3. An individual and an insurer both have a utility function U(w) = ln(w).
The individual has initial wealth 10 and the insurer has initial wealth
100.
(a) Calculate the premium P that the individual would be prepared
to pay to fully insure a loss of 5 with probability 50%.
(b) Show that the premium Q that the insurer requires satisfies the
equation
Q^2 + 195Q − 500 = 0
(c) Hence find the premium that the insurer requires.
(d) Comment on the difference between P and Q.

Thanks
Greatly appreciate it

 

[Margaret Wood]

Phew! This is too big a query! The expected utility theory is covered in Chapter 5 of the Course Notes and its application to insurance is covered in Chapter 6 of the Course Notes. The questions that you ask are very similar to questions (and solutions) included in these chapters.

 

[fireranger]

Phew! This is too big a query! The expected utility theory is covered in Chapter 5 of the Course Notes and its application to insurance is covered in Chapter 6 of the Course Notes. The questions that you ask are very similar to questions (and solutions) included in these chapters.

Hi Margaret
Thanks for the reply. This might be a stupid question but where can you find the course notes.

 

[CA2 student]

Hi Margaret
Thanks for the reply. This might be a stupid question but where can you find the course notes.

http://www.acted.co.uk/Html/paper_course_notes.htm

They cost £68 though.

 

[fireranger]

Phew! This is too big a query! The expected utility theory is covered in Chapter 5 of the Course Notes and its application to insurance is covered in Chapter 6 of the Course Notes. The questions that you ask are very similar to questions (and solutions) included in these chapters.

Hi Margaret,
I cant afford these notes, but is it possible if you could check if I am doing it right. Do u first differentiate [ lnx + pln(1+αy) + (1-p)in(1-α)] wrt α and equate to 0

then u get py - 1 + p - yα =0
then u make α the subject

then u differentiate again to see if u get negative answer and if u do it means its maximised.

but i dont understand the following questions:

* when i differentiate again do I use this term: [{py(1+αy)^-1} -{(1-p)(1-α)^-1}]
or
do I use this term : py -1+ p - yα

* also what happens to U(w) = ln (w). ie whats this used for?

(b) also I dont have a clue what does the numerator stand for ie part b , because y=value increased by, p = prob of increasing and (1-p) stands for prob of it falling to 0.

(c) when it says y = doubled its value does that mean y = 2(1+y) => y = -2?

Please help me.
Thanks

 

[Anna Walklate]

Hi,

Unfortunately we can't help you directly as it would be unfair to students who purchase our materials and come along to our tutorials. But you never know, a generous student may be willing to help you out.

Anna